Numerical methods were first put into use as an effective tool for solving partial differential equations (PDEs) by John von Neumann in the mid-1940s.
In a 1949 letter von Neumann wrote “the entire computing machine is merely one component of a greater whole, namely, of the unity formed by the computing machine, the mathematical problems that go with it, and the type of planning which is called by both.
” The “greater whole” is viewed today as scientific computation: over the past sixty years, scientific computation has emerged as the most versatile tool to complement theory and experiments, and numerical methods for solving PDEs are at the heart of many of today’s advanced scientific computations.
Numerical solutions found their way from financial models on Wall Street to traffic models on Main Street. This study provide solution to partial differential equation using numerical methods.
TABLE OF CONTENTS
CHAPTER ONE: INTRODUCTION
1.1 Background of the Study
1.2 Statement of Research Problem
1.3 Aim and Objectives of Study
1.4 Scope of Study
1.5 Significance of Study
CHAPTER TWO: Literature Review
2.1 Examples of nonlinear PDEs
2.2. Examples of time-dependent PDEs. Atomic physics is dominated by the
2.3. Well-posed problems.
3.1 Numerical methods
3.1.1 Finite-difference methods.
3.1.2. Finite-element methods.
3.1.3. Finite-volume methods
3.1.4. Spectral methods.
4.0 Basic Concepts in the Analysis of Numerical Methods
4.1. Consistency and order of accuracy.
4.2. Convergence and convergence rate
4.3. Stability of numerical methods.
4.4. From the linear to the nonlinear setup.
4.5. Challenges in numerical methods for nonlinear problems.
CHAPTER FIVE: Conclusion