Numerical Methods

This book provides a thorough exploration of key topics, including interpolation, numerical integration, differential equations, and root-finding algorithms. It features practical applications and detailed, step-by-step solutions to real-world problems, ensuring a comprehensive understanding of complex concepts. With engaging examples and intuitive explanations, readers will build confidence in applying numerical methods effectively across various fields.

• Error Of Interpolation
• Relations Between Differences And Derivatives
• Newton's Forward Difference Formula
• Interpolation With Evenly Spaced Points
• Boundry Value Problem Governed By Second Order Differential Equation
• Newton's Backward Difference Interpolation Formula
• Divided Differences
• Interpolation
• Finite Difference Method
• Lagrange Interpolation
• Linear Interpolation
• Finite Difference Methods For Wave Equations
• Spline Function
• Explicit Method For Heat Conduction Equations
• Newtons Divided Difference Interpolation
• Implicit Methods Wave Equations
• Explicit Methods For Wave Equations
• Quadratic Interpolation
• Implicit Methods For Heat Conduction Equations
• Finite Difference Methods For Laplace
• Cubic Interpolation
• Truncation Error Of The Schmidt Method
• Introduction Of Boundry Value Problems
• Classification Of Linear Second Order Partial Differetiation Equation
• Truncation Error Of The Explicit Method For Wave Equation
• Finite Difference Methods For Poisson Equations
• Solution Of Algebraic And Transcendental Equations
• Guass Elimination Method
• Power Method
• Convergence Of The Iteration Methods
• Methods Of Solving Roots Of Polynomial Equations
• Newton-raphson Method
• Eigen Value Problems
• Gauss-jacobi Iteration Method
• Initial Approximation For An Iterative Procedure
• Gauss-seidel Iteration Method
• Method Of False Position
• Iterative Methods
• General Iteration Method
• Linear System Of Algebraic Equations
• Guass Jordan Method
• Direct Method For Solving Linear System
• Simpsom's 3/8 Rule
• Error In Simpson's 1/3 Rule
• Gauss-legendre Integration Rules
• Composite Simpson's 1/3 Rule
• Simpson’s 1/3 Rule
• Romberg Method For The Simpson's 1/3 Rule
• Evaluation Of Double Intergral Using Trapezium Rule
• Composite Trapezium Rule
• Romberg Method For The Trapezium Rule
• Evaluation Of Double Intergral Using Simpson's Rule
• Gauss One Point Rule (Gauss-legendre One Point Rule)
• Gauss Three Point Rule (Gauss-legendre Three Point Rule)
• Derivatives Using Newton's Backward Difference Formula
• Numerical Differentiation
• Trapezium Rule
• Gauss Two Point Rule (Gauss-legendre Two Point Rule)
• Derivatives Using Newton’s Forward Difference Formula
• Derivatives Using Divided Difference Formula
• Numerical Integration And Integration Rules Based On Uniform Mesh Spacing
• Romberg Method
• Single Step Method
• Reduction Of Second Order Equation To A First Order System
• Predictor Methods
• Milne-simpsons Method
• Taylor Series Method
• Modified Euler Or Heun’s Methods
• Stability Of Numericals Method
• Runge-kutta Fourth Order Method
• Multi Step Methods
• Taylor Series Method
• Introduction To Initial Value Problem For Ordinary Differential Equations
• Runge Kutta Methods
• Adams-moulton Methods
• Multi Step Methods And Predictor-corrector Methods