Runge Kutta Loop and save array of results to workspace

Question

Komal Rajana 2020-7-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/561461-runge-kutta-loop-and-save-array-of-results-to-workspace

评论： Komal Rajana 2020-7-8

Hello,

I would like to run the runge kutta method within a loop for various values for 'p'. My problem is saving the array of results (for outputs=Y) in the workspace for each loop/increment of 'p'. Please assist. Thank you

    function [x, y] = FunctionBeta_Executor(F)
for p=1:0.2:5
h=0.15;                                             % step size (smaller step size gives more accurate solutions)
x = 0:h:3;                                          % x space
y = zeros(length(x):1);                             % Memory allocation
y(1) = 0;       % initial condition
F = @(x, y)(x+y+p);
for i=1:(length(x)-1)                             
% i=1:(length(x)-1)                              % calculation loop
    k1 = F(x(i),y(i));
    k2 = F(x(i)+0.5*h,y(i)+0.5*h*k1);
    k3 = F((x(i)+0.5*h),(y(i)+0.5*h*k2));
    k4 = F((x(i)+h),(y(i)+k3*h));
    y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4)*h;  % main equation
 
end
figure, plot(x, y)  % To see the solution results
    end
end

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Answer 1

Alan Stevens 2020-7-8

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https://ww2.mathworks.cn/matlabcentral/answers/561461-runge-kutta-loop-and-save-array-of-results-to-workspace#answer_462764

在 MATLAB Online 中打开

Here's one way:

p=1:0.2:5;
h=0.15;                                            
x = 0:h:3;                                          
y = zeros(length(x),length(p));                      
F = @(x, y, p)(x+y+p);
for j=1:length(p)
    y(1,j) = 0;       % initial condition
   for i=1:(length(x)-1)                             
    k1 = F(x(i),y(i,j), p(j));
    k2 = F(x(i)+0.5*h, y(i,j)+0.5*h*k1, p(j));
    k3 = F((x(i)+0.5*h), y(i,j)+0.5*h*k2, p(j));
    k4 = F((x(i)+h), y(i,j)+k3*h, p(j));
    y(i+1,j) = y(i,j) + (1/6)*(k1+2*k2+2*k3+k4)*h;  % main equation
   end
end
figure, plot(x, y)  % To see the solution results