Analytical Solution of Nonlinear Dynamics of a Self-Igniting Reaction-Diffusion System Using Modified Adomian Decomposition Method

Algorithm 1

MATLAB program to find the numerical solution of nonlinear differential equation (1) when the time (𝑡) is large (or) (3).

function pdex4

m = 0;

x = linspace(0,1);

t = linspace(0,100000);

sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t);

u1 = sol(:,:,1);

u2 = sol(:,:,2);

figure

plot(x,u1(end,:))

title(‘u1(x,t)')

xlabel(‘Distance x')

ylabel(‘u1(x,2)')

%––––––––––––––––––––––––––––––––––

figure

plot(x,u2(end,:))

title(‘u2(x,t)')

xlabel(‘Distance x')

ylabel(‘u2(x,2)')

%––––––––––––––––––––––––––––––––––

function [c,f,s] = pdex4pde(x,t,u,DuDx)

c = [1; 1];

f = [1; 1].* DuDx;

l = 0.233;

p = 35000;

b = 4.287;

g = 13.6;

F = −p*u(1)*exp(−g/u(2))/l;

F1 = b*p*u(1)*exp(−g/u(2));

s = [F; F1];

%––––––––––––––––––––––––––––––––––

function u0 = pdex4ic(x);

u0 = [1; 1];

%––––––––––––––––––––––––––––––––––

function [pl,ql,pr,qr] = pdex4bc(xl,ul,xr,ur,t)

pl = [ul(1)−1; ul(2)−1];

ql = [0; 0];

pr = [0; ur(2)−1];

qr = [1; 0];