fsolve in backward euler method

2 次查看（过去 30 天）

Hrishikesh Das 2020-4-30

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/522053-fsolve-in-backward-euler-method

编辑： Hrishikesh Das 2020-4-30

Please help to implement fsolve for a third order ODE

%%
clear
close all
clc
%%
%%  The differential equation is :  x''' = 2 x'' + 6x
%Boundary condition 
%x(0) =1, x'(0) = 0, x''(0)=1,
% Changing a third order differential equation into a system of linear
% equation
%x(1) = x ; 
%%x(2) = x' = x(1)'
%x(3) = x'' = x(2)'
%x(3)' = 2 x(3) + 6 x(1)
t0 = 0;              %initial value
x0 = [1;0;1];          %initial condition(given)
tEnd = 5;            %end of time step
h = 0.001;          %step size
N = (tEnd-t0)/h;     %number of interval
T = t0:h:tEnd;
X = zeros(3, N+1); %a series of 3-element column vectors
X(:,1) = x0;
for i = 1:N
    %fi = [X(2,i);X(3,i);2*X(3,i)+6*X(1,i)]; 
    x = fsolve(@(x) x-X(:,i) - h* %%%%%%%%%); <-- problem.
    X(:, i+1) = x;
end
%%
%ploting===================================================================
plot(T,X,'.','LineWidth',2);
title('Approximate solution Euler Implicit Method')