using Matlab in science problem

I use Finite Difference Method (FDM) in two dimension in my thesis. I want to write my program for FDM method in two dimension in MATLAB, but I couldn't find suitable function for my program, for example I want to solve bellow equation by MATLAB:

   alfaf * F(ix  ,j) 
+  deltaf* F(ix-1,j)
+  miuf  * F(ix,j-1) 
-  landaf* F(ix+1,j) 
-  Af    * F(ix,j+1) 
= 0

[Rafael Freire]

witch one of the values is a constant and witch one is a variable?

[Doug Hull]

You need to give more information here. I reformated the question to be readable. What have you tried, which are the unknowns. Do you know how to write a function in MATLAB?

[Farnaz Tabatabaei]

Dear Friend;

Please find my complete program that has many errors as bellow answer.

Regards

Farnaz

[Farnaz Tabatabaei]

With many thanks for your kind reply to me, please find the program that I wrote as attached. Please be informed that my equation is a kind of partial differential equation (like laplace equation). F functions are Variable & alfaf, deltaf, miuf, Af are my constant, but they are depended on degrees.

my programm:

% edit program

% example 13900328

clc

clear all

N=input('N=');

% created Boundry condition

kk=0;

for ix=1:N-1;

for j=1:N-1;

kk=kk+1;

%kissi=input('Please input kissi: ');

%Etta=input('Please input Etta: ');

o=0.0000001;

%L=input('Please input L: ');

L=1;

%Omega=input('Please input Omega: ');

Omega=1;

%miu0=input('Please input miu0: ');

h=-pi+0.00000001;

miu0=0.74;

%epsilon0=input('Please input epsilon0: ');

epsilon0=1;

%Betta=input('Please input Betta: ');

Betta=1;

C=3*10^8;

DeltaEtta = L / (N-1);

DeltaKissi = 2 * pi /(N-1);

Etta(ix)=o+(ix-1)*DeltaEtta;

Kissi(j)=h+(j-1)*DeltaKissi;

Etta=Etta(ix);

Kissi=Kissi(j);

k(ix,j) = (2*L.^2).*(((Omega.^2).*epsilon0.*miu0.*(L^2).*(Etta^2).*(cosh(Etta)-sinh(Etta))-(Betta^2).*sinh(Etta).*(cosh(Etta)-cos(Kissi)).*(1-cosh(Etta).*cos(Kissi)))./((Omega^2).*epsilon0.*miu0.*(L^2)*sinh(Etta.^2).*(((Omega.^2)).*epsilon0.*miu0.*(L^2).*sinh(Etta.^2)-2*(Betta.^2).*(cosh(Etta)-cos(Kissi)).^2)+(Betta.^4).*(cosh(Etta)-cos(Kissi)).^4));

q(ix,j) = ((2*L.^2.*(Betta).^2.*sinh(Etta).^2.*sin(Kissi).*(cosh(Etta)-cos(Kissi)))./((Omega).^2.*epsilon0.*miu0.*L.^2.*sinh(Etta).^2.*((Omega).^2.*epsilon0.*miu0.*L.^2.*sinh(Etta).^2.-2.*(Betta).^2.*(cosh(Etta)-cos(Kissi)).^2)+(Betta).^4.*(cosh(Etta)-cos(Kissi)).^4));

GammaT2(ix,j) = ((Omega).^2.*epsilon0.*miu0-(Betta).^2.*((cosh(Etta)-cos(Kissi)).^.2./L.^2.*sinh(Etta)^2));

alfaprim(ix,j) = ((((Betta*sin(Kissi)*(cosh(Etta)-cos(Kissi))^2)/L^3*sinh(Etta))* ...

(-k(ix,j)-(q(ix,j)*(1-cosh(Etta)*cos(Kissi))/(sinh(Etta)*sin(Kissi))-(2/(GammaT2(ix,j))* ...

(DeltaEtta))-(q(ix,j)*(cosh(Etta)-cos(Kissi))/(sin(Kissi)*(DeltaEtta)))+(k(ix,j) * ...

(cosh(Etta)-cos(Kissi))/(sin(Kissi)*(DeltaKissi)))-2*(1-cosh(Etta)* ...

cos(Kissi))/(GammaT2(ix,j))* sin(Kissi)*(DeltaKissi)*sinh(Etta)*(DeltaKissi)))));

deltaprim(ix,j) = (((Betta*sin(Kissi)*(cosh(Etta)-cos(Kissi))^2)/L^3*sinh(Etta))* ...

(2/((GammaT2(ix,j))*(DeltaEtta))+q(ix,j)*(cosh(Etta)-cos(Kissi))/(sin(Kissi)*(DeltaEtta))));

miuprim(ix,j) = ((-(Betta*(cosh(Etta)-cos(Kissi))^2)/L^3*sinh(Etta))* ...

(k(ix,j)*(cosh(Etta)-cos(Kissi))/(DeltaKissi))-2*(1-cosh(Etta)*cos(Kissi)) ...

/((GammaT2(ix,j))*sinh(Etta)*(DeltaKissi)));

alfa(ix,j) = ((((Omega)*(cosh(Etta)-cos(Kissi))^2)/L^2)*((-2/((GammaT2(ix,j))*(DeltaEtta)^2)) ...

-(2/((GammaT2(ix,j))*(DeltaKissi)^2))+(k(ix,j)/(DeltaEtta))+(1-cosh(Etta)*cos(Kissi))/ ...

((GammaT2(ix,j))*sinh(Etta)*(cosh(Etta)-cos(Kissi))*(DeltaEtta))+q(ix,j)/(DeltaKissi)- ...

(sin(Kissi)/(GammaT2(ix,j)*DeltaKissi*cosh(Etta)-cos(Kissi)))));

Delta(ix,j) = ((((Omega)*(cosh(Etta)-cos(Kissi))^2)/L^2)*(1/(DeltaEtta)^2-k(ix,j)/(DeltaEtta)- ...

(1-cosh(Etta)*cos(Kissi))/((GammaT2(ix,j))*(DeltaEtta)*sinh(Etta)*(cosh(Etta) - cos(Kissi)))));

landa(ix,j) = (((Omega)*(cosh(Etta)-cos(Kissi))^2)/((L^2)*(GammaT2(ix,j))*(DeltaEtta)^2));

A(ix,j) = (((Omega)*(cosh(Etta)-cos(Kissi))^2)/((L^2)*(GammaT2(ix,j))*(DeltaKissi)^2));

miu(ix,j)=(((Omega)*(cosh(Etta)-cos(Kissi))^2)/((L^2)*(GammaT2(ix,j))*((1/(DeltaKissi)^2)- ...

(q(ix,j) /(DeltaKissi))+(sin(Kissi)/(DeltaKissi)*(GammaT2(ix,j))*(cosh(Etta)-cos(Kissi))))))

alfaf=alfaprim-i.*alfa;

Deltaf=deltaprim-i.*Delta;

miuf=miuprim-i.*miu;

landaf=i.*landa;

Af=i.*A;

%B=rand(N-1,1);

% AA=rand(N-1,N-1);

%F=rand(N-1,1);

F(ix,j)=(-1./alfaf).*(Deltaf.*F(ix-1,j)+miuf.*F(ix+1,j)-Af.*F(ix,j+1));

B(kk,1)=-subs(F(ix,j),{F(ix,j),F(ix+1,j)},{0,0});

AA(ix,j)=subs(F(ix,j),{F(ix+1,j)},{0,0})-B(kk,1);

% Boundry Condition

if (ix==1)

F(ix,j)=2*i;

if (ix==N)

F(ix,j)=3*i;

if (j==1 || j==N)

F(ix,1)=1+i*1.5;

F(ix,N)=1+i*1.5;

alfaf*F(ix,j)+Deltaf*F(ix-1,j)+miuf*F(ix,j-1)-landaf*F(ix+1,j)-Af*F(ix,j+1)==0;

end

end

end

end

end

Thank you & Best Regards

Farnaz