up Ascher docs, line width and unicode characters fixed

Author: elswit

toolbox/+otp/+ascherlineardae/+presets/Canonical.m

@@ -1,6 +1,6 @@
 classdef Canonical < otp.ascherlineardae.AscherLinearDAEProblem
-    % The problem defined by Uri Ascher in :cite:p:`Asc89` (sec. 2) 
-    % which uses timespan $t \in [0, 1]$  and intial condition $[y_0, z_0]^T = [1, \beta]^T  $.
+    % The problem defined by Uri Ascher in :cite:p:`Asc89` (sec. 2) which uses time span $t \in [0, 1]$ and intial 
+    % condition $[y_0, z_0]^T = [1, β]^T$.
     % 
     methods
         function obj = Canonical(varargin)
@@ -11,7 +11,7 @@
             % varargin
             %    A variable number of name-value pairs. The accepted names are
             %
-            %    - ``Beta`` – The parameter of the Ascher linear DAE problem.
+            %    - ``Beta`` – Value of $β$.
 
             p = inputParser;
             p.addParameter('beta', 1);

toolbox/+otp/+ascherlineardae/+presets/Petzold.m

@@ -1,7 +1,6 @@
 classdef Petzold < otp.ascherlineardae.AscherLinearDAEProblem
-    % The Petzold DAE example :cite:p:`Pet86` as a special case of the 
-    % Ascher linear DAE problem.
-    % This preset uses timespan $t \in [0, 1]$  and  $\beta = 0 $ with the initial condition $[y_0, z_0]^T = [1, 0]^T $.
+    % The Petzold DAE example :cite:p:`Pet86` as a special case of the Ascher linear DAE problem. This preset uses time
+    % span $t \in [0, 1]$ and $β = 0 $ with the initial condition $[y_0, z_0]^T = [1, 0]^T $.
     % 
     methods
         function obj = Petzold

toolbox/+otp/+ascherlineardae/+presets/Stiff.m

@@ -1,7 +1,6 @@
 classdef Stiff < otp.ascherlineardae.AscherLinearDAEProblem
-    % The Stiff example from :cite:p:`Asc89`. A variant of the 
-    % Ascher linear DAE problem
-    % which uses timespan $t \in [0, 1]$  and  $\beta = 100 $ with the initial condition $[y_0, z_0]^T = [1, 100]^T $.
+    % The Stiff example from :cite:p:`Asc89`. A variant of the Ascher linear DAE problem which uses time span 
+    % $t \in [0, 1]$ and $β = 100$ with the initial condition $[y_0, z_0]^T = [1, 100]^T$.
     % 
     methods
         function obj = Stiff

toolbox/+otp/+ascherlineardae/AscherLinearDAEParameters.m

@@ -1,8 +1,7 @@
 classdef AscherLinearDAEParameters
     % Parameters for Ascher Linear DAE problem 
     properties
-        % Beta is a scalar parameter in the linear model. It affects the stifness 
-        % of the problem.
+        % A scalar parameter $β$ in the linear model. It affects the stifness of the problem.
         Beta %MATLAB ONLY: (1,1) {mustBeNumeric} = 1
     end
 end

toolbox/+otp/+ascherlineardae/AscherLinearDAEProblem.m

@@ -1,34 +1,31 @@
 classdef AscherLinearDAEProblem < otp.Problem
     % A linear differential-algebraic problem with time-dependant mass matrix.
     %
-    % The Ascher linear DAE Problem :cite:p:`Asc89` is an index-1 differential-agebraic 
-    % equation given by
+    % The Ascher linear DAE Problem :cite:p:`Asc89` is an index-1 differential-agebraic equation given by
     %
     % $$
     % \begin{bmatrix}
     % 1 & -t \\
     % 0 & 0
     % \end{bmatrix} \begin{bmatrix} y'(t) \\ z'(t) \end{bmatrix} = \left[ \begin{array}{cc}
     % -1 & 1+t \\
-    % \beta & -1-\beta t
+    % β & -1-β t
     % \end{array}\right] \begin{bmatrix} y(t) \\ z(t) \end{bmatrix} + \begin{bmatrix}
     % 0 \\
-    % \sin t
+    % \sin(t)
     % \end{bmatrix}.
     % $$
     %
-    % When the initial condition $y(0) = 1 , z(0) = \beta$ is used, the problem has the following closed-form solution:
+    % When the initial condition $y(0) = 1 , z(0) = β$ is used, the problem has the following closed-form solution:
     %
     % $$
     % \begin{bmatrix} y(t)\\ z(t) \end{bmatrix} = \begin{bmatrix}
-    % t \sin(t) + (1 + \beta  t) e^{-t}\\
-    % \beta  e^{-t} + \sin(t)
+    % t \sin(t) + (1 + β  t) e^{-t}\\
+    % β  e^{-t} + \sin(t)
     % \end{bmatrix}.
     % $$
-    % This DAE problem 
-    % can be used to investigate
-    % the convergence of implcit time-stepping methods due to its stiffness and time-dependant mass
-    % matrix.
+    % This DAE problem can be used to investigate the convergence of implcit time-stepping methods due to its stiffness
+    % and time-dependant mass matrix.
     %
     % Notes
     % -----
@@ -37,13 +34,13 @@
     % +---------------------+-----------------------------------------+
     % | Number of Variables | 2                                       |
     % +---------------------+-----------------------------------------+
-    % | Stiff               | possibly, depending on $\beta$          |
+    % | Stiff               | possibly, depending on $β$              |
     % +---------------------+-----------------------------------------+
     %
     % Example
     % -------
     % >>> problem = otp.ascherlineardae.presets.Canonical('Beta', 50);
-    % >>> t = linspace(0,1);
+    % >>> t = linspace(0, 1);
     % >>> sol = problem.solveExactly(t);
     % >>> problem.plot(t, sol);
 
@@ -76,9 +73,9 @@ function onSettingsChanged(obj)
 
         function label = internalIndex2label(~, index)
             if index == 1
-                label = 'Differential Variable';
+                label = 'Differential';
             else
-                label = 'Algebraic Variable';
+                label = 'Algebraic';
             end
         end