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Initial Value Ordinary Differential Equations
The Initial Value Diffusion Problem
The Initial Value Transport and Wave Problems
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absolute value applied approximate approximate solution assumed backward difference band bound boundary conditions boundary value problem calculated called characteristic chosen coefficients compared components consider constant CONTINUE convergence defined depends derivatives determine diagonal difference method diffusion DIMENSION dx dy dz eigenvalue equal evaluated exact solution example explicit method fact factor Figure finite difference formula functions Galerkin given gives IMPLICIT DOUBLE initial value integrals iteration known less linear system matrix maximum multiple nonlinear nonzero Note ordinary differential equation PARAMETER partial differential equation pivoting polynomial positive positive-definite region roots satisfies shown shows side solution solve solver space stability starting step stepsize stiff subroutine symmetric Table term Theorem tk+1 trial triangle triangular tridiagonal truncation error U(Xi unknowns vector verify X X X zero