Numerical Methods for Initial Value Problems in Ordinary Differential Equations
eBook - PDF

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

  1. 308 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

About this book

Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

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Yes, you can access Numerical Methods for Initial Value Problems in Ordinary Differential Equations by Simeon Ola Fatunla, Werner Rheinboldt,Daniel Siewiorek in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780122499302
eBook ISBN
9781483269269
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Numerical Methods for Initial Value Problems in Ordinary Differential Equations
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. CHAPTER 1. PRELIMINARIES
  7. CHAPTER 2. NUMERICAL INTEGRATION ALGORITHMS
  8. CHAPTER 3. THEORY OF ONE-STEP METHODS
  9. CHAPTER 4. RUNGE-KUTTA PROCESSES
  10. CHAPTER 5. LINEAR MULTISTEP METHODS
  11. CHAPTER 6. NUMERICAL TREATMENT OF SINGULAR/ DISCONTINUOUS INITIAL VALUE PROBLEMS
  12. CHAPTER 7. EXTRAPOLATION PROCESSES AND SINGULARITIES
  13. CHAPTER 8. STIFF INITIAL VALUE PROBLEMS
  14. CHAPTER 9. STIFF ALGORITHMS
  15. CHAPTER 10. SECOND ORDER DIFFERENTIAL EQUATIONS
  16. CHAPTER 11. RECENT DEVELOPMENTS IN ODE SOLVERS
  17. REFERENCES
  18. INDEX