Numerical Integration of Bivariate Functions Using Fluctuationlessness Theorem with a Trigonometric Basis Function to Deal with Highly Oscillatory Functions

Abstract

Fluctuation free matrix representation developed recently and successfully applied to many integration involving problem can also be used in approximating the multiple remainder terms of the integral of the Multivariate Taylor expansion. This provides us with a new numerical integration method for multivariate functions. However in this paper, instead of a polynomial basis set which would spoil an approximation to the integration of highly oscillatory functions, a mixture of trigonometric functions and polynomials is chosen as basis set such that high oscillations are somehow imitated by the basis function structures to get high efficiency.