Fourth Order Conservative Exponential Methods for Linear Evolution Equations

One - way Large Range Step Methods forHelmholtz

A useful approach for long range computation of the Helmholtz equation in a waveguide is to re-formulate it as the operator diierential Riccati equation for the Dirichlet-to-Neumann (DtN) map. For waveguides with slow range dependence, the piecewise range independent approximation is used to derive a second order range stepping method for this one-way re-formulation. The range marching formulas...

A Derivative-free Fourth Order Exponential Method for Linear Evolution Equations

STABILITY ANALYSIS FROM FOURTH ORDER NONLINEAR EVOLUTION EQUATIONS FOR TWO CAPILLARY GRAVITY WAVE PACKETS IN THE PRESENCE OF WIND OWING OVER WATER.

Asymptotically exact and nonlocal fourth order nonlinear evolution equations are derived for two coupled fourth order nonlinear evolution equations have been derived in deep water for two capillary-gravity wave packets propagating in the same direction in the presence of wind flowing over water.We have used a general method, based on Zakharov integral equation.On the basis of these evolution eq...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...