Mathematics B series / J. C. butcher / Ainyu Mitsui

Product description ※Please note that product information is not in full comprehensive meaning because of the machine translation.

Mathematics
Introduction
Initial-value problems have applications in applied mathematics, engineering, physics and other sciences, and although it is crucial to find reliable and efficient numerical solutions for their solutions, the mathematical problems concerning initial-value problems and their approximate solutions can be effectively divided into two parts by their nature : problems concerning analytical functions and problems concerning the sequence of coefficients that are algebraic in nature.
In this book, we examine the accuracy of numerical solutions by examining the formal Taylor expansions of solutions and their numerical approximations.
Contents
Introduction
Table of Contents
Introduction
Table of Contents
Introduction
Table of Contents
>
1.2 Differential equations
1.3 Examples of differential equations
1.4 Euler method
1.5 Differential equations
1.6 Multi-value method
1.7 B-series analysis of numerical solutions
Chapter 2 Trees and forests
2.1 Trees, graphs and forests Introduction
2.2 Rooted trees and free (rooted) trees
2.3 Forests and forests
2.4 Tree space and forest space
Synthesis of 3.9 B Series
Chapter 4 Algebraic Analysis and Universal Integration Method
4.1 Introduction
4.2 Universal Integration Method
4.3 Runge-Kutta Equivalence and Reducibility
4.4 Universal Integration Method Equivalence and Reducibility
4.5 Synthesis of Runge-Kutta Method
4.6 Synthesis of Universal Integration Method
4.7 B Group and subgroup
4.8 subgroup B ^? and B ^ 0 Linear Operators
Chapter 5 B Series and Runge-Kutta Method
5.1 Introduction
5.2 Degree Analysis for Scalar Problems
5.3 Runge-Kutta Method
5.4 Explicit Runge-Kutta Method
5.6 Implicit Runge-Kutta Method
5.7 Effective Degree Method
Chapter 6 General Linear Multi-Step Method
6.4 Formulation of General Linear Method
6.3 Motivation for General Linear Method <1.1 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 5.5 6.1 6.2 6.5 6.6 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9