Skip to content

Commit 96e1350

Browse files
tamaskistamaskis
committed
update before redefining how time is kept
1 parent aaf33e7 commit 96e1350

File tree

93 files changed

+2547
-665
lines changed

Some content is hidden

Large Commits have some content hidden by default. Use the searchbox below for content that may be hidden.

93 files changed

+2547
-665
lines changed

‎docs/AB2_doc.html‎

Lines changed: 188 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,188 @@
1+
2+
<!DOCTYPE html
3+
PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
4+
<html><head>
5+
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
6+
<!--
7+
This HTML was auto-generated from MATLAB code.
8+
To make changes, update the MATLAB code and republish this document.
9+
--><title>AB2</title><meta name="generator" content="MATLAB 9.11"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2022-06-06"><meta name="DC.source" content="AB2_doc.m"><style type="text/css">
10+
html,body,div,span,applet,object,iframe,h1,h2,h3,h4,h5,h6,p,blockquote,pre,a,abbr,acronym,address,big,cite,code,del,dfn,em,font,img,ins,kbd,q,s,samp,small,strike,strong,tt,var,b,u,i,center,dl,dt,dd,ol,ul,li,fieldset,form,label,legend,table,caption,tbody,tfoot,thead,tr,th,td{margin:0;padding:0;border:0;outline:0;font-size:100%;vertical-align:baseline;background:transparent}body{line-height:1}ol,ul{list-style:none}blockquote,q{quotes:none}blockquote:before,blockquote:after,q:before,q:after{content:'';content:none}:focus{outine:0}ins{text-decoration:none}del{text-decoration:line-through}table{border-collapse:collapse;border-spacing:0}
11+
12+
html { min-height:100%; margin-bottom:1px; }
13+
html body { height:100%; margin:0px; font-family:Arial, Helvetica, sans-serif; font-size:10px; color:#000; line-height:140%; background:#fff none; overflow-y:scroll; }
14+
html body td { vertical-align:top; text-align:left; }
15+
16+
h1 { padding:0px; margin:0px 0px 25px; font-family:Arial, Helvetica, sans-serif; font-size:1.5em; color:#d55000; line-height:100%; font-weight:normal; }
17+
h2 { padding:0px; margin:0px 0px 8px; font-family:Arial, Helvetica, sans-serif; font-size:1.2em; color:#000; font-weight:bold; line-height:140%; border-bottom:1px solid #d6d4d4; display:block; }
18+
h3 { padding:0px; margin:0px 0px 5px; font-family:Arial, Helvetica, sans-serif; font-size:1.1em; color:#000; font-weight:bold; line-height:140%; }
19+
20+
a { color:#005fce; text-decoration:none; }
21+
a:hover { color:#005fce; text-decoration:underline; }
22+
a:visited { color:#004aa0; text-decoration:none; }
23+
24+
p { padding:0px; margin:0px 0px 20px; }
25+
img { padding:0px; margin:0px 0px 20px; border:none; }
26+
p img, pre img, tt img, li img, h1 img, h2 img { margin-bottom:0px; }
27+
28+
ul { padding:0px; margin:0px 0px 20px 23px; list-style:square; }
29+
ul li { padding:0px; margin:0px 0px 7px 0px; }
30+
ul li ul { padding:5px 0px 0px; margin:0px 0px 7px 23px; }
31+
ul li ol li { list-style:decimal; }
32+
ol { padding:0px; margin:0px 0px 20px 0px; list-style:decimal; }
33+
ol li { padding:0px; margin:0px 0px 7px 23px; list-style-type:decimal; }
34+
ol li ol { padding:5px 0px 0px; margin:0px 0px 7px 0px; }
35+
ol li ol li { list-style-type:lower-alpha; }
36+
ol li ul { padding-top:7px; }
37+
ol li ul li { list-style:square; }
38+
39+
.content { font-size:1.2em; line-height:140%; padding: 20px; }
40+
41+
pre, code { font-size:12px; }
42+
tt { font-size: 1.2em; }
43+
pre { margin:0px 0px 20px; }
44+
pre.codeinput { padding:10px; border:1px solid #d3d3d3; background:#f7f7f7; }
45+
pre.codeoutput { padding:10px 11px; margin:0px 0px 20px; color:#4c4c4c; }
46+
pre.error { color:red; }
47+
48+
@media print { pre.codeinput, pre.codeoutput { word-wrap:break-word; width:100%; } }
49+
50+
span.keyword { color:#0000FF }
51+
span.comment { color:#228B22 }
52+
span.string { color:#A020F0 }
53+
span.untermstring { color:#B20000 }
54+
span.syscmd { color:#B28C00 }
55+
span.typesection { color:#A0522D }
56+
57+
.footer { width:auto; padding:10px 0px; margin:25px 0px 0px; border-top:1px dotted #878787; font-size:0.8em; line-height:140%; font-style:italic; color:#878787; text-align:left; float:none; }
58+
.footer p { margin:0px; }
59+
.footer a { color:#878787; }
60+
.footer a:hover { color:#878787; text-decoration:underline; }
61+
.footer a:visited { color:#878787; }
62+
63+
table th { padding:7px 5px; text-align:left; vertical-align:middle; border: 1px solid #d6d4d4; font-weight:bold; }
64+
table td { padding:7px 5px; text-align:left; vertical-align:top; border:1px solid #d6d4d4; }
65+
66+
67+
68+
69+
70+
</style></head><body><div class="content"><h1><tt>AB2</tt></h1><!--introduction--><p>Propagates the state vector forward one time step using the Adams-Bashforth 2nd-order method.</p><p><a href="index.html">Back to IVP Solver Toolbox Contents</a>.</p><!--/introduction--><h2>Contents</h2><div><ul><li><a href="#1">Syntax</a></li><li><a href="#2">Description</a></li><li><a href="#3">Input/Output Parameters</a></li><li><a href="#4">See also</a></li></ul></div><h2 id="1">Syntax</h2><pre class="language-matlab">F = AB2(f,t,F,h)
71+
</pre><h2 id="2">Description</h2><p><tt>F = AB2(f,t,y,h)</tt> updates the <img src="AB2_doc_eq03148538246847756930.png" alt="$\mathbf{F}$" style="width:8px;height:8px;"> matrix, <tt>F</tt>, for the next sample time, given the <img src="AB2_doc_eq03148538246847756930.png" alt="$\mathbf{F}$" style="width:8px;height:8px;"> matrix at time <tt>t</tt>, the function <tt>f(t,y)</tt> defining the ODE <img src="AB2_doc_eq13964145860186194730.png" alt="$\dot{\mathbf{y}}=\mathbf{f}(t,\mathbf{y})$" style="width:50px;height:11px;">, and the step size <tt>h</tt>.</p><h2 id="3">Input/Output Parameters</h2><p>
72+
<table border=1>
73+
<tr>
74+
<td></td>
75+
<td style="text-align:center"><b>Variable</b></td>
76+
<td style="text-align:center"><b>Symbol</b></td>
77+
<td style="text-align:center"><b>Description</b></td>
78+
<td style="text-align:center"><b>Format</b></td>
79+
</tr>
80+
<tr>
81+
<td rowspan="4" style="text-align:center"><b>Input</b></td>
82+
<td style="text-align:center"><TT>f</TT></td>
83+
<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(t,\mathbf{y})" title="" /></td>
84+
<td>multivariate, vector-valued function (<img
85+
src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\rightarrow\mathbb{R}^{p}"
86+
title="" />) defining the ordinary differential equation <img src="https://latex.codecogs.com/svg.latex?\inline&space;\frac{d\mathbf{y}}{dt}=\mathbf{f}(t,\mathbf{y})" title="" />
87+
<BR> - inputs to <TT>f</TT> are the current time (<TT>t</TT>, 1×1 double) and the current state vector (<TT>y</TT>, p×1 double)
88+
<BR> - output of <TT>f</TT> is the state vector derivative (<TT>dydt</TT>, p×1 double) at the current time/state</td>
89+
<td style="text-align:center">1×1<BR>function_handle</td>
90+
</tr>
91+
<tr>
92+
<td style="text-align:center"><TT>t</TT></td>
93+
<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;t_{n}" title="" /></td>
94+
<td>current sample time</td>
95+
<td style="text-align:center">1×1<BR>double</td>
96+
</tr>
97+
<tr>
98+
<td style="text-align:center"><TT>F</TT></td>
99+
<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /></td>
100+
<td><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /> matrix (see Section 3.5.2 of the <a href="https://tamaskis.github.io/documentation/Solving_Initial_Value_Problems_for_ODEs.pdf">technical documentation</a>)for the current sample time</td>
101+
<td style="text-align:center">p×3<BR>double</td>
102+
</tr>
103+
<tr>
104+
<td style="text-align:center"><TT>h</TT></td>
105+
<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="h" /></td>
106+
<td>step size</td>
107+
<td style="text-align:center">1×1<BR>double</td>
108+
</tr>
109+
<tr>
110+
<td rowspan="1" style="text-align:center"><b>Output</b></td>
111+
<td style="text-align:center"><TT>F</TT></td>
112+
<td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /></td>
113+
<td><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /> matrix (see Section 3.5.2 of the <a href="https://tamaskis.github.io/documentation/Solving_Initial_Value_Problems_for_ODEs.pdf">technical documentation</a>)for the next sample time</td>
114+
<td style="text-align:center">p×3<BR>double</td>
115+
</tr>
116+
</table>
117+
</p><h2 id="4">See also</h2><p><a href="AB2_doc.html"><tt>AB2</tt></a> | <a href="AB3_doc.html"><tt>AB3</tt></a> | <a href="AB4_doc.html"><tt>AB4</tt></a> | <a href="AB5_doc.html"><tt>AB5</tt></a> | <a href="AB6_doc.html"><tt>AB6</tt></a> | <a href="AB7_doc.html"><tt>AB7</tt></a> | <a href="AB8_doc.html"><tt>AB8</tt></a></p><p class="footer"><br><a href="https://www.mathworks.com/products/matlab/">Published with MATLAB&reg; R2021b</a><br></p></div><!--
118+
##### SOURCE BEGIN #####
119+
%% |AB2|
120+
% Propagates the state vector forward one time step using the
121+
% Adams-Bashforth 2nd-order method.
122+
%
123+
% <index.html Back to IVP Solver Toolbox Contents>.
124+
%% Syntax
125+
% F = AB2(f,t,F,h)
126+
%% Description
127+
% |F = AB2(f,t,y,h)| updates the $\mathbf{F}$ matrix, |F|, for the next
128+
% sample time, given the $\mathbf{F}$ matrix at time |t|, the function
129+
% |f(t,y)| defining the ODE $\dot{\mathbf{y}}=\mathbf{f}(t,\mathbf{y})$,
130+
% and the step size |h|.
131+
%% Input/Output Parameters
132+
% <html>
133+
% <table border=1>
134+
% <tr>
135+
% <td></td>
136+
% <td style="text-align:center"><b>Variable</b></td>
137+
% <td style="text-align:center"><b>Symbol</b></td>
138+
% <td style="text-align:center"><b>Description</b></td>
139+
% <td style="text-align:center"><b>Format</b></td>
140+
% </tr>
141+
% <tr>
142+
% <td rowspan="4" style="text-align:center"><b>Input</b></td>
143+
% <td style="text-align:center"><TT>f</TT></td>
144+
% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}(t,\mathbf{y})" title="" /></td>
145+
% <td>multivariate, vector-valued function (<img
146+
% src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{f}:\mathbb{R}\times\mathbb{R}^{p}\rightarrow\mathbb{R}^{p}"
147+
% title="" />) defining the ordinary differential equation <img src="https://latex.codecogs.com/svg.latex?\inline&space;\frac{d\mathbf{y}}{dt}=\mathbf{f}(t,\mathbf{y})" title="" />
148+
% <BR> - inputs to <TT>f</TT> are the current time (<TT>t</TT>, 1×1 double) and the current state vector (<TT>y</TT>, p×1 double)
149+
% <BR> - output of <TT>f</TT> is the state vector derivative (<TT>dydt</TT>, p×1 double) at the current time/state</td>
150+
% <td style="text-align:center">1×1<BR>function_handle</td>
151+
% </tr>
152+
% <tr>
153+
% <td style="text-align:center"><TT>t</TT></td>
154+
% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;t_{n}" title="" /></td>
155+
% <td>current sample time</td>
156+
% <td style="text-align:center">1×1<BR>double</td>
157+
% </tr>
158+
% <tr>
159+
% <td style="text-align:center"><TT>F</TT></td>
160+
% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /></td>
161+
% <td><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /> matrix (see Section 3.5.2 of the <a href="https://tamaskis.github.io/documentation/Solving_Initial_Value_Problems_for_ODEs.pdf">technical documentation</a>)for the current sample time</td>
162+
% <td style="text-align:center">p×3<BR>double</td>
163+
% </tr>
164+
% <tr>
165+
% <td style="text-align:center"><TT>h</TT></td>
166+
% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;h" title="h" /></td>
167+
% <td>step size</td>
168+
% <td style="text-align:center">1×1<BR>double</td>
169+
% </tr>
170+
% <tr>
171+
% <td rowspan="1" style="text-align:center"><b>Output</b></td>
172+
% <td style="text-align:center"><TT>F</TT></td>
173+
% <td style="text-align:center"><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /></td>
174+
% <td><img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{F}" title="" /> matrix (see Section 3.5.2 of the <a href="https://tamaskis.github.io/documentation/Solving_Initial_Value_Problems_for_ODEs.pdf">technical documentation</a>)for the next sample time</td>
175+
% <td style="text-align:center">p×3<BR>double</td>
176+
% </tr>
177+
% </table>
178+
% </html>
179+
%% See also
180+
% <AB2_doc.html |AB2|> |
181+
% <AB3_doc.html |AB3|> |
182+
% <AB4_doc.html |AB4|> |
183+
% <AB5_doc.html |AB5|> |
184+
% <AB6_doc.html |AB6|> |
185+
% <AB7_doc.html |AB7|> |
186+
% <AB8_doc.html |AB8|>
187+
##### SOURCE END #####
188+
--></body></html>

‎docs/AB2_doc_eq03148538246847756930.png‎

468 Bytes
Loading

‎docs/AB2_doc_eq13964145860186194730.png‎

2.23 KB
Loading

0 commit comments

Comments
 (0)