## 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.

### MSC:

 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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