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  • Boundry value Problems in Ordinary Differential Equation and Initial and Boundry value problem in partial differential Equation
    • Introduction of Boundry value Problems
    • Boundry Value problem governed by Second order Differential Equation
    • Finite Difference method
    • Classification of Linear Second Order Partial Differetiation Equation
    • Finite Difference Methods for Laplace
    • Finite Difference Methods for poisson Equations
    • Finite Difference Methods for Heat Conduction Equations
    • Explicit Method for Heat Conduction Equations
    • Truncation error of the Schmidt method
    • Implicit methods for Heat Conduction Equations
    • Finite Difference Methods for Wave Equations
    • Explicit methods for Wave Equations
    • Truncation error of the explicit method for wave equation
    • Implicit methods Wave Equations

  • Solution of equation and eigen value problems  
    • Solution of algebraic and transcendental equations
    • Methods of solving roots of polynomial equations
    • Initial Approximation for an Iterative Procedure
    • Method of False Position
    • Newton-Raphson Method
    • General Iteration Method
    • Convergence of the Iteration Methods
    • Linear system of algebraic equations
    • Direct method for solving linear system
    • Guass elimination method
    • guass jordan method
    • Iterative Methods
    • Gauss-Jacobi Iteration Method
    • Gauss-Seidel Iteration Method
    • Eigen value problems
    • Power method

  • Interpolation and Approximation
    • Interpolation
    • Lagrange Interpolation
    • Linear Interpolation
    • Quadratic interpolation
    • Error of interpolation
    • Divided differences
    • Newton’s Divided Difference Interpolation
    • Interpolation With Evenly Spaced Points
    • Relations between differences and derivatives
    • Newton's forward difference formula
    • Newton's Backward Difference Interpolation Formula
    • Spline function
    • Cubic Interpolation

  • Numerical Differentiation And Integration
    • Numerical Differentiation
    • Derivatives Using Newton’s Forward Difference Formula
    • Derivatives Using Newton's Backward difference Formula
    • Derivatives using Divided Difference Formula
    • Numerical Integration and Integration Rules Based on Uniform Mesh Spacing
    • Trapezium Rule
    • Error in Trapezium Rule
    • Composite trapezium rule
    • Simpson’s 1/3 Rule
    • Error in Simpson's 1/3 Rule
    • Composite Simpson's 1/3 Rule
    • Simpsom's 3/8 Rule
    • Romberg Method
    • Romberg method for the trapezium rule
    • Romberg method for the Simpson's 1/3 Rule
    • Gauss-Legendre Integration Rules
    • Gauss one point rule (Gauss-Legendre one point rule)
    • Gauss Two point rule (Gauss-Legendre Two point rule)
    • Gauss Three point rule (Gauss-Legendre Three point rule)
    • Evaluation of Double Intergral Using Trapezium Rule
    • Evaluation of Double Intergral Using Simpson's rule

  • Initial Value Problem for Ordinary Differential Equations
    • Introduction to Initial Value Problem for Ordinary Differential Equations
    • Reduction of second order equation to a first order system
    • Single Step Method
    • Multi step Methods
    • Taylor series Method
    • Modified Euler or Heun’s Methods
    • Runge Kutta Methods
    • Taylor Series Method
    • Runge-Kutta Fourth Order Method
    • Predictor Methods (Adams-Bashforth Methods)
    • Multi Step Methods and Predictor-Corrector Methods
    • Predictor Methods
    • Adams-Moulton Methods
    • Milne-Simpsons Method
    • Stability of Numericals Method

Branch : Electrical and Electronics Engineering | Subject : Numerical analysis
Initial Value Problem for Ordinary Differential Equations
  • Introduction to Initial Value Problem for Ordinary Differential Equations

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  • Reduction of second order equation to a first order system

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  • Single Step Method

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  • Multi step Methods

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  • Taylor series Method

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  • Modified Euler or Heun’s Methods

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  • Runge Kutta Methods

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  • Taylor Series Method

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  • Runge-Kutta Fourth Order Method

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  • Predictor Methods (Adams-Bashforth Methods)

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  • Multi Step Methods and Predictor-Corrector Methods

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  • Predictor Methods

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  • Adams-Moulton Methods

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  • Milne-Simpsons Method

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  • Stability of Numericals Method

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