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    Numerical Solution of Freholm-Volterra Integral Equations by Using Scaling Function Interpolation Method
    Applied Mathematics (2013)
    Yousef Al-JarrahEn-Bing Lin
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    Abstract:
    Wavelet methods are a very useful tool in solving integral equations. Both scaling functions and wavelet functions are the key elements of wavelet methods. In this article, we use scaling function interpolation method to solve Volterra integral equations of the first kind, and Fredholm-Volterra integral equations. Moreover, we prove convergence theorem for the numerical solution of Volterra integral equations and Freholm-Volterra integral equations. We also present three examples of solving Volterra integral equation and one example of solving Fredholm-Volterra integral equation. Comparisons of the results with other methods are included in the examples.
    Keywords:
    Interpolation
    Topics:
    Fractional Differential Equations Solutions
    Numerical methods in engineering
    Mathematical functions and polynomials
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    Exact Solutions > Integral Equations > Linear Fredholm Integral Equations of the Second Kind and Related Integral Equations with Constant Limits of Integration > Tricomi's Equation (Tricomi's Integral Equation)
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    On the Asymptotic Solution to a Class of Linear Integral Equations
    SIAM Journal on Applied Mathematics (1988)
    A. K. Gautesen
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    Kernel (algebra)
    Integral transform
    Fredholm theory
    Fredholm determinant
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    Exact Solutions > Integral Equations > Linear Fredholm Integral Equations of the First Kind and Related Integral Equations with Constant Limits of Integration > Schlomilch Equation (Schl¨
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    Fredholm theory
    Constant (computer programming)
    Independent equation
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    Exact Solutions > Integral Equations > Linear Fredholm Integral Equations of the Second Kind and Related Integral Equations with Constant Limits of Integration > Wiener-Hopf Equation of the Second Kind
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    Fredholm theory
    Constant (computer programming)
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    Springer eBooks (1988)
    R. E. KleinmanP. A. Martin
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    Elsevier eBooks (1962)
    L. Fox
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    THE INHOMOGENEOUS INTEGRAL EQUATION WITH A SYMMETRIC KERNEL
    Elsevier eBooks (1964)
    С. Л. Соболев
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    Eigenfunction
    Fredholm theory
    Integral transform
    Fredholm determinant
    Poisson kernel
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    A new approach to the numerical solution of Fredholm-Volterra integral equations by using multiquadric quasi-interpolation
    Indian Journal of Science and Technology (2012)
    R. Ezzati
    In this paper, we introduce an approach for solving Fredholm-Volterra integral equations(FVIE) of the second kind by using Multiquadric quasi-interpolation (MQ). Approximation of unknown function is done by using expansion method based on MQ. This method obtains acceptable approximate solution using simple computations. Also we prove a theorem for convergence analysis. We test the proposed method in some examples and compare the numerical and exact results. Keywords: Radial basis function, Quasi-interpolation,Fredholm-Volterra integral equations, numerical method
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    Solvability of some partial integral equations in Hilbert space
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