Stability of Finite-difference Schemes for Semilinear Multidimensional Parabolic Equations
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Bosko Jovanovic
,
Magdalena Lapinska-Chrzczonowicz
Abstract
Abstract — We have studied the stability of finite-difference schemes approximating initial-boundary value problem (IBVP) for multidimensional parabolic equations with a nonlinear source of a power type. We have obtained simple sufficient input data conditions, in which the solutions of differential and difference problems are globally bounded for all t. It is shown that if these conditions are not satisfied, then the solution can blow-up (go to infinity) in finite time. The lower bound of the blow-up time has been determined. The stability of the difference solution has been proven. In all cases, we used the method of energy inequalities based on the application of the Chaplygin comparison theorem for nonlinear ODEs, Bihari-type inequalities and their discrete analogs.
© Institute of Mathematics, NAS of Belarus
Articles in the same Issue
- Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems
- Stability of a Numerical Method for a Space-time-fractional Telegraph Equation
- Stability of Finite-difference Schemes for Semilinear Multidimensional Parabolic Equations
- Equal-order Finite Elements for the Hydrostatic Stokes Problem
- The Transmission Problem for the Helmholtz Equation in R³
- Efficient Halley-like Methods for the Inclusion of Multiple Zeros of Polynomials
Articles in the same Issue
- Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems
- Stability of a Numerical Method for a Space-time-fractional Telegraph Equation
- Stability of Finite-difference Schemes for Semilinear Multidimensional Parabolic Equations
- Equal-order Finite Elements for the Hydrostatic Stokes Problem
- The Transmission Problem for the Helmholtz Equation in R³
- Efficient Halley-like Methods for the Inclusion of Multiple Zeros of Polynomials
