Matlab - solucion exacta de una funcion de 2 variables

M=10; N=10;

h=0.1;k=0.1;

m=M+1; n=N;

D=0.05;

alf=5;

bet=4;

x=(0:M)*h ;t=(0:n)*k;

u=@(x,t) (2*D*bet*pi*sin(pi*x)*exp(-D*pi*pi*t))./(alf+bet*cos(pi*x)*exp(-D*pi*pi*t)) ; %solucion exata

for it=1:m-1

%fprintf('\n t x  u(anal) err\n');

for i=1:n

u(it,i)=(2*D*bet*pi*sin(pi*x(it))*exp(-D*pi*pi*t(i)))./(alf+bet*cos(pi*x(it))*exp(-D*pi*pi*t(i)));

end

end

for it=1:m-1

    fprintf('\n t \t  x  \t u  \n');

for i=1:n

fprintf('%6.2f %6.1f %15.6f  \n',t(it),x(i),u(it,i));

end

end

clear

M=10; N=10;

h=0.1;k=0.1;

m=M+1; n=N;

D=0.05;

alf=5;

bet=4;

x=(0:M)*h ;t=(0:n)*k;

u=@(x,t) (2*D*bet*pi*sin(pi*x)*exp(-D*pi*pi*t))./(alf+bet*cos(pi*x)*exp(-D*pi*pi*t)) ; %solucion exata

for it=1:m-1

%fprintf('\n t x u(anal) err\n');

    for i=1:n

    uu(it,i)=(2*D*bet*pi*sin(pi*x(it))*exp(-D*pi*pi*t(i)))./(alf+bet*cos(pi*x(it))*exp(-D*pi*pi*t(i)));

    end

end

for it=1:m-1

fprintf('\n t \t x \t u \n');

for i=1:n

fprintf('%6.2f %6.1f %15.6f \n',t(it),x(i),uu(it,i));

end

end

>> comparar_soluciones

 t 	 x 	 u

  0.00    0.0        0.000000

  0.00    0.1        0.000000

  0.00    0.2        0.000000

  0.00    0.3        0.000000

  0.00    0.4        0.000000

  0.00    0.5        0.000000

  0.00    0.6        0.000000

  0.00    0.7        0.000000

  0.00    0.8        0.000000

  0.00    0.9        0.000000

 t 	 x 	 u

  0.10    0.0        0.044106

  0.10    0.1        0.042875

  0.10    0.2        0.041653

  0.10    0.3        0.040442

  0.10    0.4        0.039243

  0.10    0.5        0.038058

  0.10    0.6        0.036888

  0.10    0.7        0.035733

  0.10    0.8        0.034596

  0.10    0.9        0.033476

 t 	 x 	 u

  0.20    0.0        0.089683

  0.20    0.1        0.087011

  0.20    0.2        0.084370

  0.20    0.3        0.081762

  0.20    0.4        0.079191

  0.20    0.5        0.076659

  0.20    0.6        0.074167

  0.20    0.7        0.071718

  0.20    0.8        0.069314

  0.20    0.9        0.066955

fprintf('%7.3f %7.3f %15.6f \n',t(it),x(i),uu(it,i));