反应扩散方程Matlab编程>> function fd1d_predator_prey ( )% FD1D_PREDATOR_PREY.m one-dimensional finite-difference method for Scheme 2% applied to the predator-prey system with Kinetics 1.%% Author:%% Marcus Garvie%%% User inputs of parameters%

反应扩散方程Matlab编程>> function fd1d_predator_prey ( )% FD1D_PREDATOR_PREY.m one-dimensional finite-difference method for Scheme 2% applied to the predator-prey system with Kinetics 1.%% Author:%% Marcus Garvie%%% User inputs of parameters%
反应扩散方程Matlab编程
>> function fd1d_predator_prey ( )
% FD1D_PREDATOR_PREY.m one-dimensional finite-difference method for Scheme 2
% applied to the predator-prey system with Kinetics 1.
%
% Author:
%
% Marcus Garvie
%
%
% User inputs of parameters
%
alpha = input('Enter parameter alpha ');
beta = input('Enter parameter beta ');
gamma = input('Enter parameter gamma ');
delta = input('Enter parameter delta ');
a = input('Enter a in [a,b] ');
b = input('Enter b in [a,b] ');
h = input('Enter space-step h ');
T = input('Enter maximum time T ');
delt = input('Enter time-step Delta t ');
%
% User inputs of initial data
%
u0 = input('Enter initial data function u0(x) ','s'); % see notes
v0 = input('Enter initial data function v0(x) ','s'); % in text
%
% Calculate some constants
%
mu=delt/(h^2);
J=round((b-a)/h);
n = J+1; % no.of nodes (d.f.) for each dependent variable
N=round(T/delt);
%
% Initialization
%
u=zeros(n,1); v=zeros(n,1); F=zeros(n,1); G=zeros(n,1);
y1=zeros(n,1); y2=zeros(n,1); z1=zeros(n,1); z2=zeros(n,1);
B1=sparse(n,n); B2=sparse(n,n); L=sparse(n,n); Lower1=sparse(n,n);
Lower2=sparse(n,n); U1=sparse(n,n); U2=sparse(n,n);
%
% Assign initial data
%
indexI=[1:n]';
x=(indexI-1)*h+a; % vector of x values on grid
u = eval(u0).*ones(n,1); v = eval(v0).*ones(n,1);
%
% Construct matrix L (without 1/h^2 factor)
%
L=sparse(1,2,-2,n,n);
L=L+sparse(n,n-1,-2,n,n);
L=L+sparse(2:n-1,3:n,-1,n,n);
L=L+sparse(2:n-1,1:n-2,-1,n,n);
L=L+sparse(1:n,1:n,2,n,n);
%
% Construct matrices B1 & B2
%
B1=sparse(1:n,1:n,1,n,n) + mu*L;
B2=sparse(1:n,1:n,1,n,n) + delta*mu*L;
%
% Perform the LU factorisation of B1 and B2
%
[Lower1,Upper1]=lu(B1);
[Lower2,Upper2]=lu(B2);
%
% Time-stepping procedure
%
for nt=1:N
% Evaluate modified functional response
hhat = u./(alpha + abs(u));
% Update right-hand-side of linear system
F = u - u.*abs(u) - v.*hhat;
G = beta*v.*hhat - gamma*v;
y1 = u + delt*F;
y2 = v + delt*G;
% Forward substitution to solve Lower1*z1=y1 for z1
z1 = Lower1\y1;
% Back-substitution to solve Upper1*u=z1 for u
u = Upper1\z1;
% Forward substitution to solve Lower2*z2=y2 for z2
z2 = Lower2\y2;
% Back-substitution to solve Upper2*v=z2 for v
v = Upper2\z2;
end
%
% Plot solution at time level T=N*delt
%
plot(x,u,'k'); hold on; plot(x,v,'k-.')
return
end
function fd1d_predator_prey ( )
|
Error:Function definitions are not permitted at the prompt or in scripts.
>>

反应扩散方程Matlab编程>> function fd1d_predator_prey ( )% FD1D_PREDATOR_PREY.m one-dimensional finite-difference method for Scheme 2% applied to the predator-prey system with Kinetics 1.%% Author:%% Marcus Garvie%%% User inputs of parameters%
1
将代码保存为M文件
2
将下面的代码复制到命令窗口,按回车键,运行即可
fd1d_predator_prey