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Iyengar S.R.K., Jain R.K. Numerical Methods

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Iyengar S.R.K., Jain R.K. Numerical Methods
New Delhi: New Age, 2009. — 326 p.
Contents:
Preface
Solution of Equations and Eigenvalue Problems

Solution of Algebraic and Transcendental Equations
Introduction
Initial Approximation for an Iterative Procedure
Method of False Position
Newton-Raphson Method
General Iteration Method
Convergence of Iteration Methods
Linear System of Algebraic Equations
Introduction
Direct Methods
Gauss Elimination Method
Gauss-Jordan Method
Inverse of a Matrix by Gauss-Jordan Method
Iterative Methods
Gauss-Jacobi Iteration Method
Gauss-Seidel Iteration Method
Eigen Value Problems
Introduction
Power Method
Answers and Hints
Interpolation and Approximation
Introduction
Interpolation with Unevenly Spaced Points
Lagrange Interpolation
Newton’s Divided Difference Interpolation
Interpolation with Evenly Spaced Points
Newton’s Forward Difference Interpolation Formula
Newton’s Backward Difference Interpolation Formula
Spline Interpolation and Cubic Splines
Answers and Hints
NUMERICAL DIFFERENTIATION AND INTEGRATION –
Introduction
Numerical Differentiation
Methods Based on Finite Differences
Derivatives Using Newton’s Forward Difference Formula
Derivatives Using Newton’s Backward Difference Formula
Derivatives Using Newton’s Divided Difference Formula
Numerical Integration
Introduction
Integration Rules Based on Uniform Mesh Spacing
Trapezium Rule
Simpson’s 1/3 Rule
Simpson’s 3/8 Rule
Romberg Method
Integration Rules Based on Non-uniform Mesh Spacing
Gauss-Legendre Integration Rules
Evaluation of Double Integrals
Evaluation of Double Integrals Using Trapezium Rule
Evaluation of Double Integrals by Simpson’s Rule
Answers and Hints
Initial Value Problems for Ordinary Differential Equations

Introduction
Single Step and Multi Step Methods
Taylor Series Method
Modified Euler and Heun’s Methods
Runge-Kutta Methods
System of First Order Initial Value Problems
Taylor Series Method
Runge-Kutta Fourth Order Method
Multi Step Methods and Predictor-Corrector Methods
Predictor Methods (Adams-Bashforth Methods)
Corrector Methods
Adams-Moulton Methods
Milne-Simpson Methods
Predictor-Corrector Methods
Stability of Numerical Methods
Answers and Hints

Boundary Value Problems in Ordinary Differential Equations and Initial & Boundary Value Problems in Partial Differential Equations
Introduction
Boundary Value Problems Governed by Second Order Ordinary Differential Equations
Classification of Linear Second Order Partial Differential Equations
Finite Difference Methods for Laplace and Poisson Equations
Finite Difference Method for Heat Conduction Equation
Finite Difference Method for Wave Equation
Answers and Hints
Bibliography
Index
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