Numerical Techniques

Contents

1. Algebraic and Transcendental Equation

1. Introduction to Error

2. Algebraic and Transcendental Equation

3. Regula-Falsi Method (The Method of False Positions)

4. Newton Raphson Method

2. Calculus of Finite Differences and Interpolation

1. Differences

2. Forward Difference

3. Backward Difference Operator

4. Central Differences

5. Other Difference

6. Properties of Operators

7. Relation between Operators

8. Fundamental Theorem on Differences of Polynomial

9. Interpolation

10.Newton-Gregory Formula for Forward Interpolation

11.Newton’s –Gregory Formula for Backward Interpolation

12.Interpolation with Unequal Interval

13.Lagrange’s Interpolation Formula

14.Divided Differences

15.Newton’s Divided Difference Formula (Interpolation with Unequal Intervals)

3. Numerical Integration

1. Introduction

2. General Quadrature Formula (For Equidistant Arguments)

3. Trapezoidal Rule

4. Simpson’s 1/3rd Rule

5. Simpson’s 3/8th Rule

6. Euler-Maclaurin’s Formula

4. Numerical Solution of Ordinary Differential Equation

1. Introduction

2. Euler’s Method

3. Euler’s Modified Method

4. Runge – Kutta Methods