On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients

• Published in: Journal of computational and applied mathematics Vol. 72; no. 2; pp. 421 - 431
• Main Authors: Mohanty, R.K., Jain, M.K., George, Kochurani
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 13.08.1996; Elsevier
• Subjects: Difference and functional equations, recurrence relations; Difference method; Exact sciences and technology; Hyperbolic equation; Linear stability; Mathematics; Maximum absolute errors; Nonlinear wave equation; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Polar coordinates; Sciences and techniques of general use; Nonlinear wave equation; Maximum absolute errors; Polar coordinates; Hyperbolic equation; Linear stability; Difference method; CR:G1.8; 65M10; Wave equation; Spherical symmetry; Second order equation; Nonlinear equations; Boundary value problems; Difference scheme; Cylindrical symmetry; Numerical integration; Grid pattern; Partial differential equations; Error estimation; Initial value problem; Absolute error; Dirichlet problem
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/0377-0427(96)00011-8

Implicit difference schemes of O( k 4 + k 2 h 2 + h 4), where k0, h 0 are grid sizes in time and space coordinates respectively, are developed for the efficient numerical integration of the system of one space second order nonlinear hyperbolic equations with variable coefficients subject to appropriate initial and Dirichlet boundary conditions. The proposed difference method for a scalar equation is applied for the wave equation in cylindrical and spherical symmetry. The numerical examples are given to illustrate the fourth order convergence of the methods.