Please enable JavaScript.

Coggle requires JavaScript to display documents.

Integral Equation, Prepared by: Muhammad Zeeshan Raza Registration No…

- - - - Series Solution Method
        
        When Kernel is degenerate one.
        Can be applied to Non Linear Volterra Integral Equation.
      - Successive Approximation Method
        
        Gives solution in series form.
      - Variational Iteration Method
        
        Can be applied To ODE,PDE and Integro Differential Equation.
        First have to convert Volterra Integral Equation into integro Differential Equation.
        Converges fastly if exact solution exists.
        Can also be used for non linear Volterra Integral Equation.
      - Successive Substitution Method
        
        Gives series solution.
        The computational work in this method is huge.
      - Converting into IVP(ODE)
        
        Use Complimentary and Particular Solution method.
        or use Variational Iteration Method.
        Gives exact solution directly.
      - Laplace Transformation Method
        
        When we have difference Kernel.
        Applicable on Volterra Integral Equation of 1st and 2nd kind and also on Volterra integro differential equation.
      - The Adomian Decomposition Method
        
        When Kernel is degenerate one.
        Much easier. We have to integrate fewer terms.
        Can be applied to all kind of Linear,non linear, differential, integral and integro differential equation.
  - - - Convert To 2nd kind
      - Convert to IBVP using integration.
        
        Complimentary Particular Solution method
      - The series solution method
      - The Adomian decomposition method
      - Variational Iteration Method
  - - - Converting 1st kind into 2nd kind
        
        Convert Non Linear Volterra Integral Equation of 1st kind into Linear Volterra Integral Equation of 2nd Kind
      - The Series solution Method
      - Laplace Transformation Method
- - - - The Method of Regularization
        
        Transfer 1st kind to 2nd Kind
        
        Transfer non-linear Fredholm integral Equation of 1st kind into Linear Fredholm integral Equation of 2nd kind
  - - - The Adomian Decomposition Method
      - The Variational Iteration Method
      - The Direct Computation Method
        
        Can be applied to both Linear and non linear and integro Fredholm integral Equation
      - The Successive Approximation
      - The Successive Substitution Method
      - Convert into BVP
        
        Use Complimentary and Particular Solution method