A non-linear hyperbolic equation

Differential Transform Method to two-dimensional non-linear wave equation

In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

Iterative methods for solving non linear Fokker-Planck equation

Image Zooming using Non-linear Partial Differential Equation

The main issue in any image zooming techniques is to preserve the structure of the zoomed image. The zoomed image may suffer from the discontinuities in the soft regions and edges; it may contain artifacts, such as image blurring and blocky, and staircase effects. This paper presents a novel image zooming technique using Partial Differential Equations (PDEs). It combines a non-linear Fourth-ord...

High Order Variable Mesh Approximation for the Solution of 1D Non-linear Hyperbolic Equation

In this paper, we propose a new high order Numerov type three-level implicit compact discretization on a non-uniform mesh for the solution of one-space dimensional non-linear hyperbolic partial differential equation of the form utt = uxx + g(x, t, u, ux, ut) subject to appropriate initial and Dirichlet boundary conditions. We use only three evaluations of the function g and three grid points at...

A non-linear Black-Scholes equation

The field of mathematical finance has gained significant attention since Black and Scholes (1973) published their Nobel Prize work in 1973. Using some simplifying economic assumptions, they derived a linear partial differential equation (PDE) of convection–diffusion type which can be applied to the pricing of options. The solution of the linear PDE can be obtained analytically. In this paper we...