LS-SVR-based solving Volterra integral equations
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Volterra equations
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.
Interpolation
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As an important type of integral equation, Volterra integral equations snatch the focus of many scientists and mathematicians to provide approximate or exact solutions to such equations. The integral transform capability of providing an algebraic solution to the integral equations led the mathematical community to lean heavily on them to solve those kinds of equations, including the Volterra integrodifferential equations of the second kind. This paper uses the complex SEE integral transform to find the exact solution to the second kind linear Volterra integrodifferential equation. The capability and efficiency of complex SEE integral transform in providing an exact solution with the minimum number of computations possible are demonstrated via practical applications.
Integral transform
Algebraic equation
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The authors study the problem for solving the system of Volterra-Fredholm Integral Equations in the space L2[a, b]. By the method of project and iteration, the system of integral equations is transformed to the linear integral equation to slove system of the integral equations.
Fredholm theory
Integral transform
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Volterra equations
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In this paper, a new integral transform, called Kharrat-Toma transform is used for solving convolution type linear Volterra integral equations of the rst kind and also convolution type linear Volterra integral equation of the second kind. Some applications are given to explain the procedure of solution of linear Volterra integral equations using Kharrat-Toma transform.
Integral transform
Convolution (computer science)
Volterra equations
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We prove that the solutions of a certain family of Volterra integrodifferential equations are uniformly bounded. We use this result to determine the asymptotic behavior of the solution of a Volterra equation in Hilbert space.
Volterra equations
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Stratonovich integral
Improper integral
Independent equation
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In this study we use triangular basis function set to solve second kind fuzzy integral equation that can be converted to a system of two integral equations in crisp case. We also consider collocation method for approximately solving the equation.
Collocation (remote sensing)
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Improper integral
Independent equation
Stratonovich integral
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This study are related Volterra integral equation with a polar kernel. Initial value problems for hyperbolic equations with function coefficients provides integral equation with 3-D Volterra type. Existence and uniqueness theorems of the Volterra integral equation a polar kernel are proved. Method of successive approximation used in the solutions of singular integral equations, existence and uniqueness theorems are emphasized
Kernel (algebra)
Volterra equations
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