Numerical Analysis of Ordinary and Delay Differential Equations 9789811992629, 9789811992636

166 109 2MB

English Pages 119 Year 2023

Numerical Analysis of Ordinary and Delay Differential Equations
9789811992629, 9789811992636

Author / Uploaded
Taketomo Mitsui
Guang-Da Hu

Table of contents :
Preface
Contents
1 Introduction
1.1 Mathematical Modelling by Differential Equations
1.2 Analytical Versus Numerical Solutions
2 Initial-Value Problems of Differential Equations: Theory
2.1 Existence and Uniqueness of Solution
2.2 Dependence on the Initial Value
2.3 Stability of Solution
3 Runge–Kutta Methods for ODEs
3.1 Runge–Kutta Methods for ODEs
3.2 Embedded Pair of Runge–Kutta Schemes
3.3 Linear Stability of Runge–Kutta Methods for ODEs
3.4 Implicit Runge–Kutta Methods
4 Polynomial Interpolation
4.1 Polynomial Interpolation and Its Algorithms
4.2 Error in Polynomial Interpolation
5 Linear Multistep Methods for ODEs
5.1 Linear Multistep Methods for ODEs
5.2 Implementation Issues of Linear Multistep Methods
5.3 Linear Stability of Linear Multistep Methods for ODEs
6 Analytical Theory of Delay Differential Equations
6.1 Differential Equation with Delay
6.2 Analytical Solution of DDEs
6.3 Linear Stability of DDEs
7 Numerical Solution of DDEs and Its Stability Analysis
7.1 Numerical DDEs
7.2 Continuous Extension of RK
7.3 Linear Stability of RK for DDEs
Bibliography
Index

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