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A matrix constructive method for the analytic-numerical solution of coupled partial differential systems. (English) Zbl 0841.65087
The paper considers analytic-numerical methods for initial-boundary problems for systems of the following type \(u_t - Au_{xx} - Bu = 0\), where \(B\) is an arbitrary square matrix and \(A\) has a positive definite symmetric part. Dirichlet boundary conditions are considered and a method related to separation of variables is introduced. The method is based on truncation of the infinite series and its analysis substantially uses the smoothing property of the parabolic equation.
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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