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updated examples, reorganized functions, updated solve_ivp
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‎examples/example_brute_force.m‎

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% Example of a "brute force" method for solving IVPs.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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n = n+1;
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end
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% trims arrays
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t = t(1:(n-1));
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x = x(1:(n-1));

‎examples/example_define_ivp.m‎

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%% example_define_ivp.m
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% IVP Solver Toolbox
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%
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% Example of defining an IVP.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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%% SCRIPT SETUP
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% clears Workspace and Command Window, closes all figures
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clear; clc; close all;
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%% SOLUTION
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% parameters
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b = 5; % damping constant [N.s/m]
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k = 1; % spring constant [N/m]
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m = 2; % mass [kg]
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x0 = 1; % initial position [m]
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dx0 = 0; % initial velocity [m/s]
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% forcing function
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F = @(t) cos(pi*t);
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% initial condition
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y0 = [x0;
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dx0];
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% ODE
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f = @(t,y) [y(2);
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-(b/m)*y(2)-(k/m)*y(1)+(1/m)*F(t)];
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%% ALTERNATE SOLUTION
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% parameters
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b = 5; % damping constant [N.s/m]
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k = 1; % spring constant [N/m]
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m = 2; % mass [kg]
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x0 = 1; % initial position [m]
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dx0 = 0; % initial velocity [m/s]
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% forcing function
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F = @(t) cos(pi*t);
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% initial condition
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y0 = [x0;
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dx0];
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% assigns function handle to ODE
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f = @(t,y) f_extra(t,y,b,k,m,F);
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% defines ODE
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function dy = f_extra(t,y,b,k,m,F)
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% unpacks state vector
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x = y(1);
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xdot = y(2);
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% preallocates state vector derivative
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dy = zeros(size(y));
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% assembles state vector derivative
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dy(1) = xdot;
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dy(2) = -(b/m)*xdot-(k/m)*x+(1/m)*F(t);
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end

‎examples/example_lorenz.m‎

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% the thumbnail image for the IVP solver toolbox.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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x(1)*x(2)-beta*x(3)];
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% solution
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[t,y] = odeabm(f,[0,100],[0;1;1.05],0.001);
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[t,y] = solve_ivp(f,[0,100],[0;1;1.05],0.001,'ABM8');
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% plots figure
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figure;

‎examples/example_matrix_ode.m‎

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% equation).
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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f = odefun_mat2vec(F);
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% final condition
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yT = odeIC_mat2vec(PT);
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yT = ivpIC_mat2vec(PT);
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% solves vector-valued IVP using a step size of h = 0.001
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[~,y] = RK4(f,[T,0],yT,0.001);
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[~,y] = solve_ivp(f,[T,0],yT,0.001,'RK4');
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% transforms solution matrix for vector-valued IVP into solution array for
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% matrix-valued IVP
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P = odesol_vec2mat(y);
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P = ivpsol_vec2mat(y);
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% solution for P0 (will be at end of array since P solved for backwards in
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% time)
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% store initial condition
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P(:,:,1) = PT;
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% solving using "RK4_step"
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% solving using "RK4"
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for i = 1:(length(t)-1)
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P(:,:,i+1) = RK4_step(F,t(i),P(:,:,i),h);
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P(:,:,i+1) = RK4(F,t(i),P(:,:,i),h);
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end
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% solution for P0 using one-step propagation

‎examples/example_pass_extra.m‎

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%% example_pass_extra.m
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% IVP Solver Toolbox
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%
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% Example of passing extra parameters to a function defining an IVP.
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% Example of passing extra parameters to functions.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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%% SOLUTION
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%% EXAMPLE #1
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% parameters
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b = 5; % damping constant [N.s/m]
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k = 1; % spring constant [N/m]
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m = 2; % mass [kg]
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x0 = 1; % initial position [m]
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dx0 = 0; % initial velocity [m/s]
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% function definition
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a = 5; b = 5; c = 5; d = 5;
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f = @(x,y) -a*(x-b)^2-c*(y-d)^2;
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% forcing function
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F = @(t) cos(pi*t);
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% call function, update "a", then call function again
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f(2,2)
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a = 20;
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f(2,2)
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% initial condition
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y0 = [x0;
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dx0];
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% NOTE: Both evaluations of "f" yield the same result.
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% differential equation
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f = @(t,y) [y(2);
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-(b/m)*y(2)-(k/m)*y(1)+(1/m)*F(t)];
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%% EXAMPLE #2
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%% ALTERNATE SOLUTION
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% original function definition
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a = 5; b = 5; c = 5; d = 5;
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f = @(x,y) -a*(x-b)^2-c*(y-d)^2;
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f(2,2)
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% parameters
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b = 5; % damping constant [N.s/m]
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k = 1; % spring constant [N/m]
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m = 2; % mass [kg]
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x0 = 1; % initial position [m]
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dx0 = 0; % initial velocity [m/s]
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% update values of constants
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a = 10; b = 10; c = 10; d = 10;
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f = @(x,y) -a*(x-b)^2-c*(y-d)^2;
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f(2,2)
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% forcing function
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F = @(t) cos(pi*t);
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% NOTE: The two evaluations of "f" no longer yield the same result.
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% initial condition
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y0 = [x0;
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dx0];
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% assigns function handle to differential equation
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f = @(t,y) f_extra(t,y,b,k,m,F);
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% defines differential equation
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function dy = f_extra(t,y,b,k,m,F)
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%% EXAMPLE #3
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% unpacks state vector
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x = y(1);
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xdot = y(2);
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% preallocates state vector derivative
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dy = zeros(size(y));
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% assembles state vector derivative
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dy(1) = xdot;
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dy(2) = -(b/m)*xdot-(k/m)*x+(1/m)*F(t);
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end
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% define function where constants can vary as well
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f_extra = @(x,y,a,b,c,d) -a*(x-b)^2-c*(y-d)^2;
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% define original function by assigning function handle to f_extra
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f = @(x,y) f_extra(x,y,5,5,5,5);
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f(2,2)
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% update values of constants
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f = @(x,y) f_extra(x,y,10,10,10,10);
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f(2,2)
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% NOTE: This example is an alternate solution to Example #2.
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%% EXAMPLE #4
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% sets values of constants
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a = 10; b = 10; c = 10; d = 10;
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f = @(x,y) f_extra2(x,y,a,b,c,d);
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f(2,2)
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% MATLAB function must be declared at end
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function f = f_extra2(x,y,a,b,c,d)
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f = -a*(x-b)^2-c*(y-d)^2;
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end
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% NOTE: This example is an alternate solution to the second part of
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% Example #2.

‎examples/example_return_extra.m‎

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% Example of returning extra parameters from an IVP solution.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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‎examples/example_waitbar.m‎

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% Examples demonstrating how to use waitbar.
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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%% EXAMPLE #1 - WAITBAR WITH DEFAULT MESSAGE
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% solves IVP, displaying waitbar with default message
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[t,y] = ABM8(f,[0,200],[0;1;1.05],0.001,true);
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% solves IVP using RK4, displaying waitbar with default message
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[t,y] = solve_ivp(f,[0,200],[0;1;1.05],0.001,[],true);
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%% EXAMPLE #2 - WAITBAR WITH CUSTOM MESSAGE
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% solves IVP, displaying waitbar with custom message
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[t,y] = ABM8(f,[0,200],[0;1;1.05],0.001,'Solving Lorenz system...');
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% solves IVP using ABM8, displaying waitbar with custom message
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[t,y] = solve_ivp(f,[0,200],[0;1;1.05],0.001,'ABM8',...
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'Solving Lorenz system...');

toolbox/misc/expand_solution_arrays.m renamed to toolbox/ivpsolver/expand_ivp_arrays.m

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% [t_new,y_new] = expand_solution_arrays(t,y)
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%
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% Copyright © 2021 Tamas Kis
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% Last Update: 2022-06-05
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% Last Update: 2022-06-06
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% Website: https://tamaskis.github.io
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% Contact: tamas.a.kis@outlook.com
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%
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%
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%==========================================================================
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function [t_new,y_new] = expand_solution_arrays(t,y)
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t_new = [t;zeros(length(t),1)];
44-
y_new = [y,zeros(size(y,1),length(t))];
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% number of subintervals
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N = length(t)-1;
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% state dimension
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p = size(y,1);
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% expands time vector
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t_new = [t;zeros(N+1,1)];
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% expands solution matrix
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y_new = [y,zeros(p,N+1)];
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end

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