The primary focus of this paper was to develop a new technique for the numerical approximations of fourth-order

partial differential equations.

Additional topics consist of the dynamics of derivative prices, pricing derivative products using

partial differential equations, partial-integro differential equations, equivalent martingale measures, new results and tools for interest-sensitive securities, modeling term structure and related concepts, the classical and Heath-Jarrow-Morton (HJM) approach to fixed income, classical

partial differential equation analysis for interest rate derivatives, relating conditional expectations to

partial differential equations, pricing derivatives via Fourier transform technique, stopping times and American-type securities, and calibration and estimation techniques.

In the nonlinear sciences, it is well known that many nonlinear

partial differential equations are widely used to describe the complex phenomena in various fields.

Introduction To

Partial Differential Equations With MATLAB, second edition

Nonlinear

partial differential equations and hyperbolic wave phenomena; proceedings.

Developed from the authors' combined total of 50 years of teaching experience, this book presents the finite element method formulated as a general purpose numerical procedure for solving engineering problems, governed by

partial differential equations.

From a script written by the user, the software performs the operations necessary to turn a description of a

partial differential equations system into a finite element model, solve the system and present graphical output of the results.

Lions, 37, specializes in nonlinear

partial differential equations.

This textbook is for an introductory course in

partial differential equations for fourth-year undergraduate or first-year graduate mathematics students, says Craig.

The Brusselator model, the nonlinear system of

partial differential equations, arises in the modeling of certain chemical reaction-diffusion processes.

In this paper we investigate the quantitative behavior of a wide range of numerical methods for solving linear

partial differential equations [PDE's].

In this section we established an Algorithm using Laplace Decomposition method on the

partial differential equations which were nonlinear.