A matrix constructive method for the analytic-numerical solution of coupled partial differential systems
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.
scientific article; zbMATH DE number 845878
scientific article