Runge-Kutta method

Question

Aslam Ali 2020-8-6

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https://ww2.mathworks.cn/matlabcentral/answers/576007-runge-kutta-method

评论： John D'Errico 2020-8-15

Write the Matlab / C++ routine of Runge-Kutta method of Order four for the following problem

y^'-y=3x^2,y(0)=4

for the range 0.1≤x≤0.5, by taking h=0.025.

Note: Please give proper answer, this question is fro numerical analysis.

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Aslam Ali 2020-8-6

I can't attempt this question because i didn't understand it please if anyone know the answer and code then kinly share it

Steven Lord 2020-8-6

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

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Answer 1

esat gulhan 2020-8-15

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https://ww2.mathworks.cn/matlabcentral/answers/576007-runge-kutta-method#answer_480402

在 MATLAB Online 中打开

%RUNGE KUTTA METHOD OF ORDER FOUR
clc;clear;                                               % Clears the screen
h=0.025;                                             % step size
x = 0.1:h:0.5;                                        
y = zeros(1,length(x));
y(1) = 4;                                          % initial condition,y(1) is y(0) value
F_xy = @(x,y) 3*x^2+y;                    % function 
for i=1:(length(x)-1)                              % calculation loop
    k_1 = F_xy(x(i),y(i));
    k_2 = F_xy(x(i)+0.5*h,y(i)+0.5*h*k_1);
    k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));
    k_4 = F_xy((x(i)+h),(y(i)+k_3*h));
    y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h;  % main equation
end
for i=1:(length(x))  
fprintf('%12.5f',x(i),y(i));fprintf('\n')
end