ODE vs. fde12 (solve fractional differential equation)

Hello,

Thanks for contributing fde12. I'm trying to solve a set of coupled equations containing fractional derivatives. To validate that I'm using it correctly, I tested on a simple problem using ODE and fde12 (with alpha=1.0). I would have expected the same result. Unfortunately, they don't. The ODE output makes sense but fde12 output blows up quickly. I'm not sure if I'm using it correctly. Any advice you can provide would be greatly appreciated. Thank you.

-Sheldon

Here's the reaction I'm solving:

A + B < ---- > AB (kon=forward, koff=backward)

| k_el (rate of elimination for B)

V

(nil)

The code I'm running is:

format compact
k_el = 1.7; 
kon = 100; 
koff = 2.5; 

% function definition
myfun = @(t,y) [-kon*y(1)*y(2) + koff*y(3);
    -kon*y(1)*y(2) + koff*y(3) - k_el*y(2);
    kon*y(1)*y(2) - koff*y(3)];

% using ODE
tspan = [0, 50];
tic; sol = ode23t(myfun,tspan,[4;2.5;0]); toc;
figure(1); plot(sol.x,sol.y); legend; grid;

% using fde12
t0=0; tfinal=50; 
h=2^(-6); alpha=1.0;
tic; [t, qsol]=fde12(alpha,myfun,t0,tfinal,[4;2.5;0],h); toc;
figure(2); plot(t,qsol(1,:)); legend; grid;

Answer 1

[Kavya Vuriti]

Assuming y(1),y(2) and y(3) are the first, second and third order derivatives of y, ode23t function has the ability to solve higher order differential equations. For solving these multiterm fractional differential equations, refer to the following function which may solve your problem:

https://www.mathworks.com/matlabcentral/fileexchange/66603-solving-multiterm-fractional-differential-equations-fde

[Sheldon Park]

Thanks for your input. Just to clarify, y(1), y(2), and y(3) are NOT the 1st, 2nd, 3rd derivatives. Rather, they are three separate variables corresponding to A, B, and AB. I am working with a set of three coupled differential equations, where the first derivative of each, e.g. dA/dt, is expressed as a function of all three original variables, A, B and AB.

[Ramashis Banerjee]

Could anyone tell me how to solve terminal value problem(integrating backward in time) using the same code??Please help me to solve it numerically.

Reach me at [e-mail]

Thank you in advance.