- Cover
- Title Page
- Contents
- Preface
- About the Authors
- Acknowledgements
- CHAPTER 1 ERRORS IN NUMERICAL COMPUTATIONS
- CHAPTER 2 SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
- 2.0. Introduction
- 2.1. Bisection Method or Bolzano Method
- 2.2. Method of False Position or Regula-Falsi (in Latin)
- 2.3. The Secant Method or the Chord Method
- 2.4. The Method of Iteration or Fixed Point Iteration: x = f (x) Method
- 2.5. Newton-Raphson Method or Newton’s Method of Finding a Root of f(x) = 0
- 2.6. Generalised Newton-Raphson Method or Modified Newton’s Method
- 2.7. Ramanujan’s Method
- 2.8. Muller’s Method
- 2.9. Chebyshev’s Method
- 2.10. Convergence of Iteration Methods
- 2.11. Newton-Raphson Method for Non-Linear Equations in Two Variables
- 2.12 Solution of Polynomial Equations
- Short Answer Questions
- CHAPTER 3 SOLUTION OF SYSTEM OF LINEAR ALGEBRAIC EQUATIONS
- CHAPTER 4 POLYNOMIAL INTERPOLATION
- 4.0. Introduction
- 4.1. Finite Difference Operators
- 4.2. Interpolation with Equally Spaced Arguments or Interpolation with Equal Intervals
- 4.3. Central Difference Interpolation Formulae
- 4.3.1 Gauss’s Forward Formula for Interpolation
- Worked Examples
- 4.3.2 Gauss’s Backward Formula for Interpolation
- Worked Examples
- Exercises 4.3
- 4.3.3 Stirling’s Formula for Interpolation
- Worked Examples
- 4.3.4 Bessel’s Formula for Interpolation
- Worked Examples
- 4.3.5 Laplace-Everett Formula for Interpolation
- Worked Examples
- Exercises 4.4
- 4.4. Interpolation with Unequal Intervals
- 4.5. Errors in Interpolation Formulae
- 4.6. Interpolation with a Cubic Spline
- Short Answer Questions
- CHAPTER 5 INVERSE INTERPOLATION
- CHAPTER 6 NUMERICAL DIFFERENTIATION
- CHAPTER 7 NUMERICAL INTEGRATION
- 7.0. Introduction
- 7.1. A General Quadrature Formula or Newton-Cotes Quadrature Formula
- 7.2. Trapezoidal Rule
- 7.3. Simpson’s Rule or Simpson’s Rule
- 7.4. Simpson’s Rule
- 7.5. Boole’s Rule
- 7.6. Weddle’s Rule
- 7.7. Error in Numerical Integration Formulae
- 7.8. Romberg’s Method for Integration
- 7.9. Two and Three Point Gaussian Quadrature Formulae
- 7.10. Euler-Maclaurin Formula for Numerical Integration
- 7.11. Double Integration
- Short Answer Questions
- CHAPTER 8 CURVE FITTING
- CHAPTER 9 INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
- 9.0. Introduction
- 9.1. Taylor’s Series Method
- 9.2. Euler’s Method and Modified Euler’s Method
- 9.3. Runge-Kutta Method (R-K Method)
- 9.4. Runge-Kutta Method for the Solution of Simultaneous Equations and Second Order Equations
- 9.5. Milne’s Predictor–Corrector Method
- 9.6. Adam’s Predictor and Corrector Method
- 9.7. Picard’s Method
- Short Answer Questions
- CHAPTER 10 BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATION
- CHAPTER 11 DIFFERENCE EQUATIONS
- 11.0 Introduction
- 11.1 Linear Difference Equation
- 11.2 Solution of a Difference Equation
- 11.3 Formation of a Difference Equation
- 11.4. Linear Homogeneous Difference Equation with Constant Coefficients
- 11.5. Some Basic Results of Difference Operator to Solve Difference Equations
- 11.6. Non-Homogeneous Linear Difference Equations with Constant Coefficients
- 11.7. First Order Linear Difference Equation with Variable Coefficients
- Short Answer Questions
- Bibliography
Numerical Analysis
P. Sivaramakrishna Das
Retired Professor and Head, Department of Mathematics
Ramakrishna Mission Vivekananda College
Chennai
Currently
Head, Department of Science and Humanities
Professor of Mathematics
KCG College of Technology
Chennai
C. Vijayakumari
Professor of Mathematics (Retired)
Queen Mary’s College (Autonomous)
Chennai
Chennai • Delhi
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