Numerical Study on Single and Multi-Dimensional Boundary Value Problems by the Method of Weighted Residual

Orthonormal Bernstein Galerkin technique for computations of higher order eigenvalue problems

“…The optimal stable, nonnegative Bernstein polynomial basis gained popularity among several researchers and useful properties have been applied to solve regular as well as singular second to higher order BVPs and eigenvalue problems [ [9] , [10] , [11] , 22 , 23 , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] ]. As stated in [22] , the polynomials can be used to form a basis over [0, 1] which is complete.…”

“…Stability and convergence measures [9] for the polynomial estimations in the Galerkin MWR have been studied by several authors [ 9 , 10 , [22] , [23] , [24] , [25] , [31] , [32] , [33] ]. Moreover, orthogonal polynomials basis can approximate general functions in Hilbert spaces.…”