Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation. (English) Zbl 1114.65347

Summary: A few explicit difference schemes are discussed for the numerical solution of the linear hyperbolic equation \(u_{tt} + 2\alpha u_{t} + \beta ^{2}u = u_{xx} + f(x, t), \alpha > 0, \beta > 0\), in the region \(\Omega = \{(x, t)\mid a < x < b, t > 0\}\) subject to appropriate initial and Dirichlet boundary conditions, where \(\alpha\) and \(\beta\) are real numbers. The proposed scheme is showed to be unconditionally stable, and a numerical result is presented.


65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L15 Initial value problems for second-order hyperbolic equations
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