Using operational matrix for solving nonlinear class of mixed Volterra–Fredholm integral equations
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DOI: 10.1002/mma.4237
Abstract: This paper presents a computational technique for the solution of the nonlinear mixed Volterra–Fredholm integral equations of the second kind. Using the properties of three-dimensional modification of hat functions, these are types of equations to… read more here.
Keywords: using operational; mixed volterra; volterra fredholm; fredholm integral ... See more keywords
Numerical solution of Volterra–Fredholm integral equations with Hosoya polynomials
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DOI: 10.1002/mma.7479
Abstract: In this study, Volterra–Fredholm integral equation is solved by Hosoya polynomials. The solutions obtained with these methods were compared on the figure and table. And error analysis was done. MATLAB programming language has been used… read more here.
Keywords: hosoya polynomials; volterra fredholm; solution volterra; numerical solution ... See more keywords
A Nyström method for a class of Fredholm integral equations on the real semiaxis
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DOI: 10.1007/s10092-016-0199-7
Abstract: A class of Fredholm integral equations of the second kind, with respect to the exponential weight function $$w(x)=\exp (-(x^{-\alpha }+x^\beta ))$$w(x)=exp(-(x-α+xβ)), $$\alpha >0$$α>0, $$\beta >1$$β>1, on $$(0,+\infty )$$(0,+∞), is considered. The kernel k(x, y) and the… read more here.
Keywords: integral equations; fredholm integral; class fredholm; nystr method ... See more keywords
Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis
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DOI: 10.1007/s40065-019-0243-y
Abstract: This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with… read more here.
Keywords: chebyshev collocation; fredholm integral; integral equation; equation ... See more keywords
LSMR iterative method for solving one- and two-dimensional linear Fredholm integral equations
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DOI: 10.1007/s40314-019-0903-8
Abstract: This paper is devoted to extend an iterative algorithm for sparse least-squares problems for solving one- and two-dimensional linear Fredholm integral equations. We consider the operator form of these equations and then develop the LSMR… read more here.
Keywords: one two; solving one; method; two dimensional ... See more keywords
On the numerical treatment and analysis of two-dimensional Fredholm integral equations using quasi-interpolant
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DOI: 10.1007/s40314-020-1129-5
Abstract: In this paper, we study the quadratic rule for the numerical solution of linear and nonlinear two-dimensional Fredholm integral equations based on spline quasi-interpolant. Also the convergence analysis of the method is given. We show… read more here.
Keywords: dimensional fredholm; analysis; quasi interpolant; two dimensional ... See more keywords
Solving Two-Dimensional Nonlinear Fredholm Integral Equations Using Rationalized Haar Functions in the Complex Plane
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DOI: 10.1007/s40819-019-0631-1
Abstract: As far as we are aware, no research has been published about two-dimensional integral equations in the complex plane by using Haar bases or any other kinds of wavelets. We introduce a numerical method to… read more here.
Keywords: integral equations; fredholm integral; equations using; complex plane ... See more keywords
Analytical Solution of Volterra–Fredholm Integral Equations Using Hybrid of the Method of Contractive Mapping and Parameter Continuation Method
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DOI: 10.1007/s40819-019-0684-1
Abstract: In this paper, an analytical method is proposed to solve Volterra–Fredholm integral equations. The method is based on a hybrid of the method of contractive mapping and parameter continuation method. The existence and uniqueness of… read more here.
Keywords: hybrid method; integral equations; fredholm integral; volterra fredholm ... See more keywords
A Numerical Method for Solving Fredholm Integral Equations of the First Kind with Logarithmic Kernels and Singular Unknown Functions
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DOI: 10.1007/s40819-020-00923-1
Abstract: In this paper, we present a numerical method for solving singular Fredholm integral equations of the first kind. The method is based on the application of the shifted Chebyshev polynomials of the second kind using two techniques.… read more here.
Keywords: kind; method; equations first; first kind ... See more keywords
Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Sinc Nyström method
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DOI: 10.1080/00207160.2017.1411591
Abstract: ABSTRACT In this paper, a double-exponential (DE) Sinc Nyström method is utilized to solve nonlinear two-dimensional Fredholm integral equations of the second kind. Using the DE transformation, the Sinc quadrature rule for a definite integral… read more here.
Keywords: nonlinear two; sinc nystr; nystr method; method ... See more keywords
On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels
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DOI: 10.1080/00207160.2019.1619705
Abstract: ABSTRACT This paper considers a special boundary element method for Fredholm integral equations of the second kind with singular and highly oscillatory kernels. To accelerate the resolution of the linear system and the matrix-vector multiplication… read more here.
Keywords: second kind; kind singular; equations second; singular highly ... See more keywords