2nd Order Nonlinear Differential Equation Solving with Central Difference Method?

Question

Furkan Celik 2019-3-1

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https://ww2.mathworks.cn/matlabcentral/answers/447689-2nd-order-nonlinear-differential-equation-solving-with-central-difference-method

评论： Torsten 2021-7-17

I am trying to solve a 2nd order non linear differential equation using central finite difference method but ı cant, it is a boundary value problem

y''+2y'+5y=8sinx+4cosx

y(0)=0 and y(30)=0

step is dx=0.5

How can ı solve it, would you give me some suggestion about that or any script ?

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Answer 1

Torsten 2019-3-1

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https://ww2.mathworks.cn/matlabcentral/answers/447689-2nd-order-nonlinear-differential-equation-solving-with-central-difference-method#answer_363346

http://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node9.html

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Answer 2

Furkan Celik 2019-3-3

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https://ww2.mathworks.cn/matlabcentral/answers/447689-2nd-order-nonlinear-differential-equation-solving-with-central-difference-method#answer_363570

编辑：Furkan Celik 2019-3-3

在 MATLAB Online 中打开

Thank you so much for your response.. Im sharing script what i did.

clear all;
clc;
x = 0:3:30;
n = length(x);
y = zeros(1,n);
y(1,1)=0;
y(1,n)=0;
A = zeros(n-2);
B = zeros(1,n-2);
for i=1:n-2;
    A(i,i) = 43;
end
for i=2:n-2;
    A(i,i-1)=-2;
    A(i-1,i)=4;
end
A
B(1,1)= 9*(8*sind(x(1,2))+4*cosd(x(1,2)));
B(1,n-2) = 9*(8*sind(x(1,n-1))+4*cosd(x(1,n-1)))
for i=2:n-3;
    B(1,i)=9*(8*sind(x(1,i+1))+4*cosd(x(1,i+1)));
end
B
BB=B';
Y = inv(A)*BB;
YY=Y'
y(1,2:n-1)=YY(1,1:n-2)
plot(x,y);