tdiffusion_dn.mac - pism - [fork] customized build of PISM, the parallel ice sheet model (tillflux branch)
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       tdiffusion_dn.mac (686B)
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            1 /* pure diffusion, Dirichlet at the base and Neumann at the surface */
            2 T(t) := exp(-(lambda*alpha)^2*t);
            3 Z(z) := A*sin(lambda*z) + B*cos(lambda*z);
            4 v(z,t) := T(t) * Z(z);
            5 
            6 phi(z) := U[0] + Q[L] * z;
            7 u(z,t) := v(z,t) + phi(z);
            8 
            9 B : 0;
           10 lambda : %pi / (2*L);
           11 
           12 /* Check that T satisfies its equation */
           13 eq_T : diff(T(t), t) + (lambda*alpha)^2 * T(t) = 0;
           14 
           15 /* Check that Z satisfies its equation */
           16 eq_Z : diff(Z(z), z, 2) + lambda^2 * Z(z) = 0;
           17 
           18 /* Check that u(x,t) satisfies the PDE */
           19 eq: diff(u(x,t),t) = alpha^2 * diff(u(x,t),x,2);
           20 lhs(eq) - rhs(eq), expand;
           21 
           22 /* Check that du/dx = Q[L] at x = L */
           23 ux_L : subst([x = L], diff(u(x,t), x));
           24 
           25 /* Check that u(0,t) = U[0] */
           26