Laplace inversion for the solution of an abstract heat equation without the forward transform of the source term
Shu‐Lin Wu · Journal of Numerical Mathematics · 2016
Abstract We consider the discretization in time of inhomogeneous parabolic equations, using the technique of Laplace inversion along a contour located in the complex left half-plane which, after transformation to a finite interval, is then evaluated to high accuracy by a contour quadrature rule. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. A serious problem is how to treat the source term