Error using sym/matlab​Function>g​etOptions "Invalid Values"

I'm trying to write a script to solve an ODE using Symbolic Math Toolbox as well as some other numerical solutions. However, when I attempt to convert the solution of the ODE into a function so that I can use it with these numerical methods I encounter an error.

close all; clc; clear;


% Constants
t0 = 1; % initial time
tf = 2; % final time
stepSize = 0.5; % step size for numerical methods

syms t y(t)  % Define symbolic variables

% MATLAB Symbolic Math Toolbox

% Define the ODE
ode = t^2*diff(y,t,2) - 2*t*diff(y,t) + 2*y == 0;

% THE ISSUE ARISES HERE
odeFunction = matlabFunction(rhs(ode), 'Vars', {t, y});

% Solve the ODE symbolically
sol = dsolve(ode);

% Display the solution
disp(sol);

% Euler's Method
[t_euler, y_euler] = Euler(odeFunction, 4, tf, stepSize);

fprintf('\n');

% Improved Euler's Method
[t_improved, y_improved] = EulersImproved(odeFunction, 4, tf, stepSize);

% Euler's function implementation.
function [t, y] = Euler(odeFunction, initialValue, targetValue, stepSize)

    % Initialize arrays to store time and solution values
    t = 1:stepSize:targetValue;
    y = zeros(size(t));

    % Set initial value
    y(1) = initialValue;

    % Euler method to solve the ODE
    for i = 1:length(t) - 1
        % Compute the next value using Euler's method
        y(i + 1) = y(i) + stepSize * odeFunction(t(i), y(i));
    end

    % Display the final result at the target value
    fprintf('The value of the equation, using Eulers Method, at x = %.2f is %.4f\n', targetValue, y(end));
end

% Improved Euler's function implementation.
function [t, y] = EulersImproved(odeFunction, initialValue, targetValue, stepSize)
    % Initialize arrays to store time and solution values
    t = 1:stepSize:targetValue;
    y = zeros(size(t));

    % Set initial value
    y(1) = initialValue;

    % Improved Euler's method to solve the ODE
    for i = 1:length(t) - 1
        % Predictor step
        y_pred = y(i) + stepSize * odeFunction(t(i), y(i));

        % Corrector step
        y(i + 1) = y(i) + 0.5 * stepSize * (odeFunction(t(i), y(i)) + odeFunction(t(i + 1), y_pred));
    end

    % Display the final result at the target value
    fprintf('The value of the equation, using the Improved Eulers Method, at x = %.2f is %.4f\n', targetValue, y(end));
end

And it gives the error:

The value of 'Vars' is invalid.

'Vars' value must be a character

vector, a 1-dimensional cell array of

character vectors, a 1-dimensional

cell array of symbolic variables or

arrays of symbolic variables, or an

array of symbolic variables.

Any help would be greatly appreciated!

[Dyuman Joshi]

% Define the ODE
ode = t^2*diff(y,t,2) - 2*t*diff(y,t) + 2*y == 0;
% THE ISSUE ARISES HERE
odeFunction = matlabFunction(rhs(ode), 'Vars', {t, y});

Why are you converting 0 (rhs of the ode) to a function?

Also, odeFunction is a function in Symbolic Math Toolbox. You should not use functions as names for variables (or scripts for that matter).

And, that function would be a better fit over matlabFunction.

[Dyuman Joshi]

Any updates, @Blake?

Answer 1

[Star Strider]

As noted, the right-hand-side of ‘ode’ is 0, and that is not actually a differential equation. The left-hand-side is.

The missing step is calling the odeToVectorField function that returns the desired result of two first-order differential equations. (Note that you need one initial condition for each differential equation.)

Since this looks like a homework assignment, I leave the rest to you —

close all; clc; clear;


% Constants
t0 = 1; % initial time
tf = 2; % final time
stepSize = 0.5; % step size for numerical methods

syms t y(t) Y % Define symbolic variables               <— CHANGED (Added 'Y') 

% MATLAB Symbolic Math Toolbox

% Define the ODE
ode = t^2*diff(y,t,2) - 2*t*diff(y,t) + 2*y == 0;

% THE ISSUE ARISES HERE
[VF,Subs] = odeToVectorField(ode)                       % <— ADDED

VF = 

Subs = 

odeFunction = matlabFunction(VF, 'Vars', {t, Y});       % — CHANGED (Changed 'Vars' Values)

odeFunction = function_handle with value:
    @(t,Y)[Y(2);1.0./t.^2.*(t.*Y(2)-Y(1)).*2.0]

% Solve the ODE symbolically
sol = dsolve(ode);

% Display the solution
disp(sol);

% Euler's Method
[t_euler, y_euler] = Euler(odeFunction, 4, tf, stepSize);

Index exceeds the number of array elements. Index must not exceed 1.

Error in sym/matlabFunction>@(t,Y)[Y(2);1.0./t.^2.*(t.*Y(2)-Y(1)).*2.0]

Error in solution>Euler (line 47)
y(i + 1) = y(i) + stepSize * odeFunction(t(i), y(i));

fprintf('\n');

% Improved Euler's Method
[t_improved, y_improved] = EulersImproved(odeFunction, 4, tf, stepSize);

% Euler's function implementation.
function [t, y] = Euler(odeFunction, initialValue, targetValue, stepSize)

    % Initialize arrays to store time and solution values
    t = 1:stepSize:targetValue;
    y = zeros(size(t));

    % Set initial value
    y(1) = initialValue;

    % Euler method to solve the ODE
    for i = 1:length(t) - 1
        % Compute the next value using Euler's method
        y(i + 1) = y(i) + stepSize * odeFunction(t(i), y(i));
    end

    % Display the final result at the target value
    fprintf('The value of the equation, using Eulers Method, at x = %.2f is %.4f\n', targetValue, y(end));
end

% Improved Euler's function implementation.
function [t, y] = EulersImproved(odeFunction, initialValue, targetValue, stepSize)
    % Initialize arrays to store time and solution values
    t = 1:stepSize:targetValue;
    y = zeros(size(t));

    % Set initial value
    y(1) = initialValue;

    % Improved Euler's method to solve the ODE
    for i = 1:length(t) - 1
        % Predictor step
        y_pred = y(i) + stepSize * odeFunction(t(i), y(i));

        % Corrector step
        y(i + 1) = y(i) + 0.5 * stepSize * (odeFunction(t(i), y(i)) + odeFunction(t(i + 1), y_pred));
    end

    % Display the final result at the target value
    fprintf('The value of the equation, using the Improved Eulers Method, at x = %.2f is %.4f\n', targetValue, y(end));
end

.

[Dyuman Joshi]

The left hand side is a differential expression, not an equation.