Meshless methods for multivariate highly oscillatory Fredholm integral equations

A local meshless method for the numerical solution of space‐dependent inverse heat problems

“…[20][21][22][23] A vast range of PDEs have been successfully solved by RBF methods. [24][25][26][27][28][29] When the goal is to approximate dispersed data in several dimensions, the RBF methods turn out to be the most suitable methodology in the case of multivariate approximation. The global, nonpolynomial, RBF method is a workable substitute for obtaining exponential accuracy (though in some cases), where the classical methods are hard to be applied.…”

Meshless approximation method of one-dimensional oscillatory Fredholm integral equations

“…Several methods are reported in the literature for numerical solution of FIE(s) [1,2,4,6,8,9,[12][13][14][15][16]. Some numerical techniques have been developed for either oscillatory integrals or non-oscillatory integral equations [7,8,14,18,20] rather than oscillatory integral equations, where the quadrature methods fails to deliver.…”

“…The main challenge of (2) is how to evaluate it accurately and efficiently especially if the KF is highly oscillatory while incorporating SP(s). The literature is adequate and very few methods have been reported in the past in this scenario, (see [1,2,4,6,9,19,20,23]).…”

“…The literature details of the evaluation methods for the models in ( 1) and ( 2) when the KF is with and free of SP(s) are given in our earlier findings [1,2,4] and the references therein. Huybrechs [8] has suggested method of steepest descent for solution of the oscillatory integrals.…”

“…The existence of the SP(s) in such models has numerous applications in the field of scattering and acoustics etc. (see [1,2,4,[6][7][8]). The proposed meshless method is accurate and cost-effective and provides a trustworthy platform to solve OFIE(s).…”