In this article,we present a numerical method to solve two-dimensional Fredholm integral equations of the second kind on general domains. The method utilizes meshless and spectralcollocationtechniquesbutitisnottraditionalmeshlesscollocationmethod.The pointinterpolationmethodwiththehelpofstrictlypositivedefiniteradialbasisfunctions isusedtoconstructshapefunctionsasabasisfunctionsintheframeofspectralcollocation methods.Thesebasisfunctions(shapefunctions)haveKroneckerdeltafunctionproperty. Sincetheproposedmethodismeshless,itdoesnotneedanydomainelementandsoitis independentofthegeometryofthedomain.Themethodreducesthesolutionofthetwo-dimensional integral equation to the solution of a linear system of algebraic equations. Convergence analysis with error estimates are given with full discussion. Furthermore, somenumericalexamplesarepresentedtoshowthevalidityandefficiencyofSMRPI.

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