An Unconditionally Stable Spline Difference Scheme for Solving the Second 2D Linear Hyperbolic Equation

Hu, Y; Liu, Huan-Wen

doi:10.1109/iccms.2010.198

Cited by 6 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been shown that the linear schemes discussed in 6, 7 are conditionally stable. In the recent past, many researchers see [8][9][10][11][12][13][14][15][16] have developed unconditionally stable implicit finite difference methods for the solution of twospace dimensional linear hyperbolic equations with significant first derivative terms. Most recently, Mohanty and Singh 17 have derived a high accuracy numerical method based on Numerov type discretization for the solution of one space dimensional nonlinear hyperbolic equations, in which they have shown that the linear scheme is unconditionally stable.…”

Section: Introductionmentioning

confidence: 99%

A New High‐Order Approximation for the Solution of Two‐Space‐Dimensional Quasilinear Hyperbolic Equations

Mohanty

Singh

2011

Advances in Mathematical Physics

View full text Add to dashboard Cite

we propose a new high-order approximation for the solution of two-space-dimensional quasilinear hyperbolic partial differential equation of the form , , , subject to appropriate initial and Dirichlet boundary conditions , where and are mesh sizes in time and space directions, respectively. We use only five evaluations of the function as compared to seven evaluations of the same function discussed by (Mohanty et al., 1996 and 2001). We describe the derivation procedure in details and also discuss how our formulation is able to handle the wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Some examples and their numerical results are provided to justify the usefulness of the proposed method.

show abstract