Weakly Singular
The Approximate Solution of Non Linear Fredholm Weakly Singular Integro-Differential equations by Using Chebyshev polynomials of the First kind
... In this paper Chebyshev polynomials of the first kind of degree n are defined in section2.In the section 3 the proposed method for solving Non linear Fredholm weakly singular integro-differential equations ...
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Some new weakly singular integral inequalities with discontinuous functions for two variables and their applications
... This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative ...
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A computational method for solving weakly singular Fredholm integral equation in reproducing kernel spaces
... In the present paper, we propose a method to solve a class of weakly singular Fredholm integral equations of the second kind in reproducing ker- nel spaces. The Taylor series of the unknown function is used ...
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Discrete collocation method for Volterra type weakly singular integral equations with logarithmic kernels
... Weakly singular integral equations with logarithmic kernels are usually difficult to solve analytically; so it is necessary to provide reliable numerical ...the singular point and extraction of the ...
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Euler Maclaurin Expansions of Errors for Multidimensional Weakly Singular Integrals and Their Splitting Extrapolation Algorithm*
... In this paper, we give the quadrature formula with the asymptotic expansions of errors for solving multidimensional integrals with arbitrary points weakly sin- gular. According to the asymptotic expansions of ...
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Bounds on some new weakly singular Wendroff type integral inequalities and applications
... to weakly singular integral inequalities in two variables and their applications to the partial differential equation with singular ...new weakly singular integral inequalities of ...
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Some new nonlinear integral inequalities with weakly singular kernel and their applications to FDEs
... which came from the study of a global existence and an exponential decay result for a parabolic Cauchy problem by Henry []. Ma and Pečarić [] used the modification of Medveď’s method [] to study some new ...
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Some new weakly singular integral inequalities and their applications to fractional differential equations
... The well-known inequalities, such as the Gronwall type inequality, the Gronwall-Bellman type inequality, the Henry-Gronwall type inequality, the Henry-Bihari type inequality and their variants in retarded form played ...
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Some New Nonlinear Weakly Singular Integral Inequalities of Wendroff Type with Applications
... In this paper, by applying Medve ˘d’s method of desingularization of weakly singular inequalities we establish some new singular version of the Wendroff inequality see 1, 12 for functions in two ...
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Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
... Monegato and Scuderi (1998) introduce a simple smoothing change of variable to solve one-dimensional linear weakly singular integral equations on bounded intervals, with input functions which may be smooth ...
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Convergence Analysis of Piecewise Polynomial Collocation Methods for System of Weakly Singular Volterra Integral Equations of The First Kind
... Abstract: We study regularity of solutions of weakly singular Volterra integral equations of the first kind. We then study the numerical analysis of discontinuous piecewise polynomial collocation methods ...
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The Approximate Solution for Solving Linear Volterra Weakly Singular Integro-Differential Equations by Using Chebyshev Polynomials of the First Kind
... In this paper, we have submitting expansion method using Chebyshev polynomials of the first kind of degree n as basis function for approximating the solution of one weakly singular integro-differential ...
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A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods
... The HAM has been shown to solve effectively, easily and accurately a large class of non- linear problems with the approximations which converge rapidly to the exact solutions. In this work, the HAM has been successfully ...
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Optimization in Transition between Two Dynamic Systems Governed by a Class of Weakly Singular Integro Differential Equations
... DOI: 10.4236/am.2019.1010059 827 Applied Mathematics is a scalar weakly singular integro-differential equation of the first kind [2] [3]. Furthermore, because of the natural facts of transition between ...
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Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications
... the weakly singular integral ...weak singular type, the second inequality was a like-weakly singular type with discontinuous functions, the third inequality was a type of weakly ...
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Estimation of unknown function of nonlinear weakly singular integral inequalities of Gronwall–Bellman–Pachpatte type
... The aim of this paper is to extend certain results that were proved in [9, 10], and general- ize (1)–(4) to some weakly singular integral inequalities. The upper bound estimations of the unknown functions ...
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Numerical Experiments on Eigenvalues of Weakly Singular Integral Equations Using Product Simpson's Rule
... The eigenvalues of (1), in general, are complex numbers, but if the kernel is Hermitian then all eigenvalues are real and the right eigenfunction is equal to the left eigenfunction corresponding to the same eigenvalue. ...
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Singularly perturbed Volterra integral equations with weakly singular kernels
... We consider finding asymptotic solutions of the singularly perturbed linear Volterra in- tegral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of ...
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A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel
... 5. Lakestani M., Nemati Saray B. and Dehghan M. Numerical solution for the weakly singular Fredholm integro- differential equations using Legendre multiwavelets, J. Comput. & Appl. Math., 235(11): ...
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On a weakly singular quadratic integral equations of Volterra type in Banach algebras
... In this paper, we present existence and uniqueness theorems of nonnegative, asymptotically stable, and ultimately nondecreasing solutions for weakly singular quadratic integral equations of Volterra type in ...
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