Bernstein polynomial multiwavelets direct method for certain physical variational problems

In this article, variational problems are solved using a direct method derived from Bernstein polynomials multiwavelets (BPMWs). Based on the BPMWs, the operational matrix of integration is provided, which converts the variational problem into an algebraic equation system. Some numerical examples are given, and their findings are compared with the exact solution and some existing methods to demonstrate the efficiency and accuracy.