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

1996 ◽  
Vol 72 (2) ◽  
pp. 421-431 ◽  
Author(s):  
R.K. Mohanty ◽  
M.K. Jain ◽  
Kochurani George
Keyword(s):  
Hyperbolic Equations ◽  
Variable Coefficients ◽  
Second Order ◽  
High Order ◽  
Nonlinear Hyperbolic Equations ◽  
Order Difference ◽  
Difference Methods

scholarly journals Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Necmettin Aggez
Keyword(s):  
Space Variable ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Integral Condition ◽  
Variable Coefficients ◽  
Difference Schemes ◽  
Order Difference ◽  
One Dimensional ◽  
Nonlocal Integral Condition ◽  
Multidimensional Hyperbolic Equations

The stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.

Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes

2011 ◽  
Vol 9 (3) ◽  
pp. 520-541 ◽  
Author(s):  
Steven Britt ◽  
Semyon Tsynkov ◽  
Eli Turkel
Keyword(s):  
Fourth Order ◽  
Finite Difference Methods ◽  
Accurate Method ◽  
Variable Coefficients ◽  
High Order ◽  
Harmonic Waves ◽  
Order Convergence ◽  
High Order Schemes ◽  
Time Harmonic ◽  
Difference Methods

AbstractIn many problems, one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method (e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing fourth order finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these problems. We present numerical results that corroborate the fourth order convergence rate for several model problems.

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