Coiflet–Galerkin method for solving second order BVPs with variable coefficients in three dimensions

Three dimensional BVPs with variable coefficients, need to evaluate a lot of complex integrals in Galerkin method solutions. We consider Coiflets, as basis functions to evaluate the complex integrals fast and effective, via three variate connection coefficients on the interval [0, 2 ⁿ ]. We show that these connection coefficients can be computed independent of n, by solving small linear systems. Moreover we prove that the rate of convergence of approximate solution to the exact solution, is O(2 ^{− nN} ) where N is the degree of Coiflets. Besides, in our proposal we do not adopt fictitious domain approach which is commonly used in wavelet‐Galerkin methods. In this way computational cost is reduced. To confirm the theoretical results, a numerical experiment is presented.