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Application of global optimization and radial basis functions to numerical solutions of weakly singular volterra integral equations

โœ Scribed by E.A Galperin; E.J Kansa

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
750 KB
Volume
43
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

novel approach to the numerical solution of weakly singular Volterra integral equations is presented using the Cm multiquadric (MQ) radial basis function (RBF) expansion rather than the more traditional finite difference, finite element, or polynomial spline schemes. To avoid the collocation procedure that is usually ill-conditioned, we used a global minimization procedure combined with the method of successive approximations that utilized a small, finite set of MQ basis functions. Accurate solutions of weakly singular Volterra integral equations are obtained with the minimal number of MQ basis functions. The expansion and optimization procedure was terminated whenever the global errors were less than 5. lo-'.

๐Ÿ“œ SIMILAR VOLUMES

Mathematical programming methods in the
Mathematical programming methods in the numerical solution of Volterra integral and integro-differential equations with weakly-singular kernel
โœ E.A. Galperin; E.J. Kansa; A. Makroglou; S.A. Nelson ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 444 KB

Nonlinear Volterra integral and integro differential equations with weakly-singular kernel are considered and solved numerically using nonlinear Mathematical programming methods based on minimax approximations. In both cases polynomial and multiquadric approximation are used.