A Weighted Least Squares Method for the Backward-Forward Heat Equation
Copyright policy )A Weighted Least Squares Method for the Backward-Forward Heat Equation
The numerical solution of the heat equation where the diffusion coefficient changes sign is treated using a weighted least squares method after the second-order equation is transformed into a first order system of symmetric-positive differential equations. Error estimates and three numerical examples are presented.
weighted least squares method, numerical examples, Error bounds for initial value and initial-boundary value problems involving PDEs, heat equation, symmetric-positive system, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, second-order equation, Initial value problems for second-order parabolic equations, Error estimates, first order system
weighted least squares method, numerical examples, Error bounds for initial value and initial-boundary value problems involving PDEs, heat equation, symmetric-positive system, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, second-order equation, Initial value problems for second-order parabolic equations, Error estimates, first order system
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