- 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
Bibliography
1. Scorborough, J.B., Numerical Mathematical Analysis. The John Hopkins University Press, Baltimore, Maryland, 1966.
2. Froberg, C.E., Introduction to Numerical Analysis, Addison-Wesley, Reading, Massachusetts, 1965.
3. Gerald, C.F. and Wheatly, P.O., Applied Numerical Analysis, Addison-Wesley, Reading, Massachusetts, 1994.
4. Hilderbrand, F.B., Introduction to Numerical Analysis, Tata McGraw Hill, New Delhi, 1982.
5. Krishnamoorthy, E.V. and Sen, S.K., Numerical Algorithms, East-West Publishers, New Delhi, 1986.
6. Johnson, L.W. and Riess, R.D., Numerical Analysis, Addison-Wesley, Reading, Massachusetts, 1982.
7. Jain, M.K., Iyengar, S.R.K. and Jain, R.K., Numerical Methods for Scientific and Engineering Computation, New Age International Publishers, New Delhi, 2003.
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