Table of Contents
Chapter 1 Solution of Algebraic and Transcendental Equations
1.1 Introduction
1.2 Gauss Elimination Method (Direct Method)
Solved Problems 1.1 to 1.2
1.3 Gauss-Jordan Method (Direct Method)
Solved Problems 1.3 to 1.6
1.4 Inverse of a Matrix by Gauss-Jordan Method (Direct Method)
Solved Problems 1.7 to 1.10
1.4.1 Errors
1.5 Iterative Method
1.5.1 Gauss-Jacobi Iterative Method
Solved Problems 1.11 to 1.13
1.5.2 Gauss-Seidel Iterative Method
Solved Problems 1.14 to 1.15
1.6 Method of Successive Approximation (Simple Iteration Method)
Solved Problems 1.16 to 1.19
1.7 Newton-Raphson Iterative Method
Solved Problems 1.20 to 1.24
1.7.1 Criterion for Convergence in Newton-Raphson Method
Solved Problems 1.25 to 1.27
1.8 EigenValue of a Matrix by Power Method
Solved Problems 1.28 to 1.32
1.9 Thomas Algorithm for Tridiagonal System of Equations
Solved Problems 1.33 to 1.35
Exercise
Multiple-Choice Questions
Exercise Problems
Chapter 2 Interpolation and Approximation
2.1 Introduction
2.2 Lagrange’s Interpolation Formula for Equal as Well as Unequal Intervals
Solved Problems 2.1 to 2.3
2.2.1 Inverse Interpolation
Solved Problem 2.4
2.3 Difference Operators
2.4 Newton’s Forward Interpolation Formula
2.5 Newton’s Backward Interpolation Formula
Solved Problems 2.5 to 2.9
2.6 Newton’s Divided Difference Formula for Interpretation
Solved Problems 2.10 to 2.12
Multiple-Choice Questions
Exercise Problems
Chapter 3 Numerical Differentiation and Integration
3.1 Introduction
3.2 Newton’s Forward Formula for Differentiation
3.3 Newton’s Backward Formula for Differentiation
Solved Problems 3.1 to 3.3
3.4 Numerical Differentiation for Unequal Intervals
Solved Problems 3.4 to 3.7
3.5 Numerical Integration
3.5.1 Trapezoidal Rule
3.5.2 Simpson’s 1/3 Rule
3.5.3 Simpson’s 3/8 Rule
Solved Problems 3.8 to 3.15
3.6 Romberg Integration
Solved Problem 3.16
3.7 Double Integration
Solved Problems 3.17 to 3.23
3.8 Two-Point and Three-Point Gaussian Quadrature Formula
Solved Problems 3.24 to 3.30
Multiple-Choice Questions
Exercise Problems
Chapter 4 Numerical Solution of Ordinary Differential
Equations
4.1 Introduction
4.2 Taylor Series Method
Solved Problems 4.1 to 4.4
4.2.1 Point wise Method in Taylor’s Series
Solved Problem 4.5
4.3 Euler’s Method
Solved Problems 4.6 to 4.8
4.4 Modified Euler’s Method
Solved Problems 4.9 to 4.10
4.5 Runge−Kutta Method of Fourth Order
Solved Problems 4.11 to 4.13
4.5.1 Runge−Kutta Method for Simultaneous First Order Differential Equation
Solved Problems 4.14 to 4.15
4.5.2 Runge−Kutta Method for Second Order Differential Equation
Solved Problem 4.16
4.6 Multi Step Methods
4.6.1 Milne’s Predictor-Corrector Method
Solved Problems 4.17 to 4.20
4.6.2 Adams−Bashforth Predictor-Corrector Method
Solved Problem 4.21
Multiple-Choice Questions
Exercise Problems
Chapter 5 Numerical Solution of Partial Differential
Equation
5.1 Introduction
5.2 Classification
Solved Problems 5.1 to 5.3
5.3 Difference Quotient
5.4 Finite Difference Formula for Two-Dimensional Heat Equation
Solved Problems 5.4 to 5.7
5.5 Poisson Equation
Solved Problems 5.8 to 5.9
5.6 One-Dimensional Wave Equation − Numerical Solution
(Hyperbolic Equation)
Solved Problems 5.10 to 5.13
5.7 One-Dimensional Heat Equation
5.7.1 Finite Difference Solution of One-Dimensional Heat Equation
5.7.2 Explicit Method
Solved Problems 5.14 to 5.15
5.7.3 Implicit Method
5.8 Crank Nicolson Method
Solved Problems 5.16 to 5.17
Multiple-Choice Questions
Exercise Problems
