Long-range numerical solution of mildly non-linear parabolic equations
We analyze the convergence of a “boundary-value” procedure for numerically solving the mildly non-linear parabolic equation,
, wherea(x, t) ≧a0>0, andf u ≧0, and the solutionu reaches a steady state ast → ∞. Such a procedure yields an error estimate, which is uniform int. We also discuss an iterative method of solving the difference equations.
$$u_t = [a (x, t) u_x ]_x + b (x, t) u_x - f(x, t, u)$$
KeywordsSteady State Error Estimate Mathematical Method Iterative Method Difference Equation
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