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

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 ?

Answer 1

[Torsten]

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

Answer 2

[Furkan Celik]

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);

[TRUONG HONG]

Can i ask a question?

how can you find A(i,i) A(i,i-1) and A(i-1,1)

Thank u

[Torsten]

All explained on the above website.

Answer 3

[Thanawut Sumtib]

Use the finite difference method to solve y'' + 2 y' − 3 y = 0 from t = 0 to 4 using a step size of 1 with y(0) = 1 and y’(0)=1.