Numerical Methods

Cover
......Page 1
Preface
......Page 6
Contents
......Page 8
1.1.1 Introduction
......Page 12
1.1.2 Initial Approximation for an Iterative Procedure
......Page 15
1.1.3 Method of False Position
......Page 17
1.1.4 Newton-Raphson Method
......Page 22
1.1.5 General Iteration Method
......Page 26
1.1.6 Convergence of the Iteration Methods
......Page 30
1.2.1 Introduction
......Page 36
1.2.2 Direct Methods
......Page 37
1.2.2.1 Gauss Elimination Method
......Page 39
1.2.2.2 Gauss-Jordan Method
......Page 44
1.2.2.3 Inverse of a Matrix by Gauss-Jordan Method
......Page 46
1.2.3.1 Gauss-Jacobi Iteration Method
......Page 52
1.2.3.2 Gauss-Seidel Iteration Method
......Page 57
1.3.1 Introduction
......Page 63
1.3.2 Power Method
......Page 64
1.4 Answers and Hints
......Page 70
2.1 Introduction
......Page 74
2.2.1 Lagrange Interpolation
......Page 75
2.2.2 Newton's Divided Difference Interpolation
......Page 83
2.3 Interpolation with Evenly Spaced Points
......Page 91
2.3.1 Newton's Forward Difference Interpolation Formula
......Page 100
2.3.2 Newton's Backward Difference Interpolation Formula
......Page 103
2.4 Spline Interpolation and Cubic Splines
......Page 110
2.5 Answers and Hints
......Page 119
3.2.1.1 Derivatives Using Newton's Forward Difference Formula
......Page 120
3.2.1.2 Derivatives Using Newton's Backward Difference Formula
......Page 128
3.2.1.3 Derivatives Using Divided Difference Formula
......Page 133
3.3.1 Introduction
......Page 139
3.3.2.1 Trapezium Rule
......Page 140
3.3.2.2 Simpson's 1/3 Rule
......Page 147
3.3.2.3 Simpson's 3/8 Rule
......Page 155
3.3.2.4 Romberg Method (Integration)
......Page 158
3.3.3 Integration Rules Based on Non-Uniform Mesh Spacing
......Page 170
3.3.3.1 Gauss-Legendre Integration Rules
......Page 171
3.3.4.1 Evaluation of Double Integrals Using Trapezium Rule
......Page 180
3.3.4.2 Evaluation of Double Integrals by Simpson's Rule
......Page 184
3.4 Answers and Hints
......Page 188
4.1 Introduction
......Page 191
4.2 Single Step and Multi Step Methods
......Page 193
4.3 Taylor Series Method
......Page 195
4.3.1 Modified Euler and Heun's Methods
......Page 203
4.4 Runge-Kutta Methods
......Page 211
4.5 System of First Order Initial Value Problems
......Page 218
4.5.2 Runge-Kutta Fourth Order Method
......Page 219
4.6 Multi Step Methods and Predictor-Corrector Methods
......Page 227
4.6.1 Predictor Methods (Adams-Bashforth Methods)
......Page 228
4.6.2.1 Adams-Moulton Methods
......Page 232
4.6.2.2 Milne-Simpson Methods
......Page 235
4.6.2.3 Predictor-Corrector Methods
......Page 236
4.7 Stability of Numerical Methods
......Page 248
4.8 Answers and Hints
......Page 249
5.2 Boundary Value Problems Governed by Second Order Ordinary Differential Equations
......Page 252
5.3 Classification of Linear Second Order Partial Differential Equations
......Page 261
5.4 Finite Difference Methods for Laplace and Poisson Equations
......Page 263
5.5 Finite Difference Method for Heat Conduction Equation
......Page 285
5.6 Finite Difference Method for Wave Equation
......Page 301
5.7 Answers and Hints
......Page 318
Bibliography
......Page 322
Index
......Page 324