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A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature. (English) Zbl 1022.65108
The paper deals with approximate solutions of the inhomogeneous parabolic problems of the form \[ u_t + Au = f(t), \quad t > 0, \qquad u(0) = u_0, \] where \(A\) is a second order elliptic differential operator with Dirichlet boundary conditions. The authors consider time discretization of (1) using a representation of the solution as an integral along a smooth curve in the complex left-half plane. The problem is reduced to a finite set of elliptic equations which are solved in parallel.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
65Y05 Parallel numerical computation
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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