Computing and Simulation for Engineers

3 A New High-Order Compact Finite Difference Scheme for One-Dimensional Helmholtz Equation using Dirichlet Boundary Conditions

Friday Ighaghai Oyakhire and Omenyi Louis

Alex Ekwueme Federal University

Jogendra Kumar

DIT University

DOI: 10.1201/9781003222255-3

CONTENTS

1. 3.1 Introduction
2. 3.2 Method
3. 3.3 Test Example
4. 3.4 Numerical Results
5. 3.5 Convergence Analysis
6. 3.6 Conclusions
7. References

3.1 Introduction

The aim of this article is to derive, implement, and test novel and improved sixth-order, eighth-order, and tenth-order compact difference schemes for solving the Helmholtz equation in one dimension using Dirichlet boundary conditions. Nowadays, there are so many powerful computing machines available, which improve the numerical techniques ...