Numerial Methods for Volterra Integral Equations with Singular Kernels

Abstract

Previous article Next article Numerial Methods for Volterra Integral Equations with Singular KernelsPeter LinzPeter Linzhttps://doi.org/10.1137/0706034PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kendall E. Atkinson, The numerical solution of Fredholm integral equations of the second kind, SIAM J. Numer. Anal., 4 (1967), 337–348 10.1137/0704029 MR0224314 0155.47404 LinkGoogle Scholar[2] H. T. Davis, The theory of Volterra integral equations of the second kind, Indiana University Studies 88–90, Bloomington, 1930 Google Scholar[3] Griffith C. Evans, Volterra's integral equation of the second kind, with discontinuous kernel, Trans. Amer. Math. Soc., 11 (1910), 393–413 MR1500871 Google Scholar[4] Avner Friedman, On integral equations of Volterra type, J. Analyse Math., 11 (1963), 381–413 MR0158232 0134.31502 CrossrefGoogle Scholar[5] A. Huber, Eine Näherungsmethode zur Auflösung Volterrascher Integralgleichungen, Monatsh. Math. Phys., 47 (1939), 240–246 10.1007/BF01695499 0021.32002 CrossrefGoogle Scholar[6] Vladimir Ivanovich Krylov, Approximate calculation of integrals, Translated by Arthur H. Stroud, The Macmillan Co., New York, 1962x+357 MR0144464 0111.31801 Google Scholar[7] N. Levinson, A nonlinear Volterra equation arising in the theory of superfluidity, J. Math. Anal. Appl., 1 (1960), 1–11 10.1016/0022-247X(60)90028-7 0094.08501 CrossrefGoogle Scholar[8] P. Linz , Masters Thesis , Numerical methods for Volterra integral equations with applications to certain boundary value problems , Doctoral thesis , University of Wisconsin , Madison , 1968 Google Scholar[9] W. Robert Mann and , František Wolf, Heat transfer between solids and gases under nonlinear boundary conditions, Quart Appl. Math., 9 (1951), 163–184 MR0042596 0043.10001 CrossrefISIGoogle Scholar[10] B. Noble, P. M. Anselone, The numerical solution of nonlinear integral equations and related topicsNonlinear Integral Equations (Proc. Advanced Seminar Conducted by Math. Research Center, U.S. Army, Univ. Wisconsin, Madison, Wis., 1963), Univ. Wisconsin Press, Madison, Wis., 1964, 215–318 MR0173369 0123.32804 Google Scholar[11] H. Oulès, Résolution numérique d'une équation intégrale singulière, Rev. Française Traitement Information Chiffres, 7 (1964), 117–124 MR0172478 0134.32901 Google Scholar[12] Komarath Padmavally, On a non-linear integral equation, J. Math. Mech., 7 (1958), 533–555 MR0103400 0082.32201 ISIGoogle Scholar[13] J. H. Roberts and , W. R. Mann, On a certain nonlinear integral equation of the Volterra type, Pacific J. Math., 1 (1951), 431–445 MR0044009 0044.32202 CrossrefGoogle Scholar[14] Carl Wagner, On the numerical solution of Volterra integral equations, J. Math. Physics, 32 (1954), 289–301 MR0060313 0055.11403 CrossrefISIGoogle Scholar[15] Andrew Young, Approximate product-integration, Proc. Roy. Soc. London Ser. A., 224 (1954), 552–561 MR0063778 0055.36001 CrossrefISIGoogle Scholar[16] Andrew Young, The application of approximate product integration to the numerical solution of integral equations, Proc. Roy. Soc. London Ser. A., 224 (1954), 561–573 MR0063779 0055.35803 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Recursive higher order fuzzy transform method for numerical solution of Volterra integral equation with singular and nonsingular kernelsJournal of Computational and Applied Mathematics, Vol. 403 Cross Ref Barycentric rational collocation methods for Volterra integral equations with weakly singular kernels25 May 2019 | Computational and Applied Mathematics, Vol. 38, No. 3 Cross Ref Stability and Convergence Analysis of a Class of Continuous Piecewise Polynomial Approximations for Time-Fractional Differential Equations2 May 2018 | Journal of Scientific Computing, Vol. 77, No. 1 Cross Ref Analytical and computational methods for a class of nonlinear singular integral equationsApplied Numerical Mathematics, Vol. 114 Cross Ref Haar wavelet method for some nonlinear Volterra integral equations of the first kindJournal of Computational and Applied Mathematics, Vol. 292 Cross Ref Resolvents for weakly singular kernels and fractional differential equationsNonlinear Analysis: Theory, Methods & Applications, Vol. 75, No. 13 Cross Ref Piecewise homotopy perturbation method for solving linear and nonlinear weakly singular VIE of second kindApplied Mathematics and Computation, Vol. 217, No. 19 Cross Ref Solution of a class of Volterra integral equations with singular and weakly singular kernelsApplied Mathematics and Computation, Vol. 199, No. 2 Cross Ref Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methodsJournal of Computational and Applied Mathematics, Vol. 140, No. 1-2 Cross Ref Further Time-Dependent Examples Cross Ref Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equationsJournal of Computational and Applied Mathematics, Vol. 115, No. 1-2 Cross Ref Mathematical programming methods in the numerical solution of Volterra integral and integro-differential equations with weakly-singular kernelNonlinear Analysis: Theory, Methods & Applications, Vol. 30, No. 3 Cross Ref An integral-spectral approach for convective-diffusive mass transfer with chemical reaction in Couette flow Mathematical formulation and numerical illustrationsChemical Engineering Journal, Vol. 68, No. 1 Cross Ref Product integration for Volterra integral equations of the second kind with weakly singular kernels1 January 1996 | Mathematics of Computation, Vol. 65, No. 215 Cross Ref AN INTEGRAL-SPECTRAL FORMULATION FOR CONVECTIVE-DIFFUSIVE TRANSPORT IN A PACKED-BED WITH ADSORPTION AT THE WALL AND BULK REACTION19 April 2007 | Chemical Engineering Communications, Vol. 138, No. 1 Cross Ref The numerical solution of Volterra integral equations with nonsmooth solutions based on sinc approximationApplied Numerical Mathematics, Vol. 9, No. 3-5 Cross Ref Numerical methods for singular nonlinear integro-differential equationsApplied Numerical Mathematics, Vol. 3, No. 3 Cross Ref Stability analysis of product ?-methods for Abel integral equations of the second kindNumerische Mathematik, Vol. 48, No. 2 Cross Ref A Comparative Survey of Numerical Methods for the Linear Generalized Abel Integral EquationZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 66, No. 3 Cross Ref On the order of the error in discretization methods for weakly singular second kind non-smooth solutionsBIT, Vol. 25, No. 4 Cross Ref Numerical solutions of Volterra integral equations with a solution dependent delayJournal of Mathematical Analysis and Applications, Vol. 112, No. 2 Cross Ref Fractional linear multistep methods for Abel-Volterra integral equations of the second kind1 January 1985 | Mathematics of Computation, Vol. 45, No. 172 Cross Ref Product integration methods for second-kind Abel integral equationsJournal of Computational and Applied Mathematics, Vol. 11, No. 1 Cross Ref The numerical solution of integral equations with weakly singular kernels15 November 2006 Cross Ref Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular KernelsHermann Brunner17 July 2006 | SIAM Journal on Numerical Analysis, Vol. 20, No. 6AbstractPDF (1325 KB)A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equationsJournal of Computational and Applied Mathematics, Vol. 8, No. 3 Cross Ref An introduction to the numerical treatment of volterra and abel-type integral equations25 August 2006 Cross Ref Micro-macropore model for sorption of water on silica gel in a dehumidifierChemical Engineering Science, Vol. 37, No. 8 Cross Ref Two species diffusion in a sphere with inter-species linkage at the boundaryComputers & Chemical Engineering, Vol. 6, No. 2 Cross Ref RADIATION PATTERNS OF AN HF VERTICAL DIPOLE NEAR A SLOPING BEACH27 February 2007 | Electromagnetics, Vol. 2, No. 2 Cross Ref Numerical solution of non-linear Volterra integral equationsJournal of Computational and Applied Mathematics, Vol. 7, No. 2 Cross Ref A recurrence relation for solution of singular Volterra integral equations using Chebyshev polynomialsBIT, Vol. 21, No. 1 Cross Ref SURFACE FIELDS AND RADIATION PATTERNS OF A VERTICAL ELECTRIC DIPOLE OVER A RADIAL-WIRE GROUND SYSTEM27 February 2007 | Electromagnetics, Vol. 1, No. 1 Cross Ref A block-by-block method for Volterra integro-differential equations with weakly-singular kernel1 January 1981 | Mathematics of Computation, Vol. 37, No. 155 Cross Ref Callocation methods for volterra integrodifferential equations with singular kernelsJournal of Computational and Applied Mathematics, Vol. 6, No. 1 Cross Ref Volterra integral equationsJournal of Soviet Mathematics, Vol. 12, No. 6 Cross Ref Discretization of Volterra integral equations of the first kind1 January 1977 | Mathematics of Computation, Vol. 31, No. 139 Cross Ref On the discretisation error of the weighted Simpson ruleBIT, Vol. 16, No. 2 Cross Ref Block methods for nonlinear Volterra integral equationsBIT, Vol. 15, No. 4 Cross Ref High Order Methods for a Class of Volterra Integral Equations with Weakly Singular KernelsFrank de Hoog and Richard Weiss14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 11, No. 6AbstractPDF (932 KB)The numerical solution of volterra intergral equations with singular kernelsBIT, Vol. 14, No. 1 Cross Ref On the Solution of a Volterra Integral Equation with a Weakly Singular KernelFrank de Hoog and Richard Weiss17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 4, No. 4AbstractPDF (768 KB)Asymptotic expansions for product integration1 January 1973 | Mathematics of Computation, Vol. 27, No. 122 Cross Ref Splinefunktionen bei der L�sung von IntegralgleichungenNumerische Mathematik, Vol. 19, No. 2 Cross Ref Volume 6, Issue 3| 1969SIAM Journal on Numerical Analysis History Submitted:07 May 1968Published online:14 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0706034Article page range:pp. 365-374ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics