A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasi-linear hyperbolic equations

作者：Mohanty Ranjan K^*; Gopal Venu

来源：Advances in Difference Equations, 2013, 2013(1): 1-20.

DOI：10.1186/1687-1847-2013-70

• second-order quasilinear hyperbolic equation
• spline in tension
• wave equation in polar coordinates
• stability analysis
• maximum absolute errors

In this paper, we propose a new three-level implicit nine-point compact finite difference formulation of order two in time and four in space directions, based on spline in tension approximation in x-direction and central finite difference approximation in t-direction for the numerical solution of one-space dimensional second-order quasi-linear hyperbolic equations with first-order space derivative term. We describe the mathematical formulation procedure in detail and also discuss how our formulation is able to handle a wave equation in polar coordinates. The proposed method, when applied to a general form of the telegrapher equation, is also shown to be unconditionally stable. Numerical examples are used to illustrate the usefulness of the proposed method.

• 出版日期2013