Spline algorithms for continuum functions
Computers in Physics
Spline algorithms for the Hartree-Fock equation for the helium ground state
Journal of Computational Physics
Integration by cell algorithm for Slater integrals in a spline basis
Journal of Computational Physics
An approximation to solutions of linear ODE by cubic interpolation
Computers & Mathematics with Applications
Operational matrices of Bernstein polynomials and their applications
International Journal of Systems Science
Hi-index | 7.29 |
An algorithm for approximating solutions to differential equations in a modified new Bernstein polynomial basis is introduced. The algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval and then makes use of the Galerkin method to determine the expansion coefficients to construct a solution. Matrix formulation is used throughout the entire procedure. However, accuracy and efficiency are dependent on the size of the set of Bernstein polynomials and the procedure is much simpler compared to the piecewise B spline method for solving differential equations. A recursive definition of the Bernstein polynomials and their derivatives are also presented. The current procedure is implemented to solve three linear equations and one nonlinear equation, and excellent agreement is found between the exact and approximate solutions. In addition, the algorithm improves the accuracy and efficiency of the traditional methods for solving differential equations that rely on much more complicated numerical techniques. This procedure has great potential to be implemented in more complex systems where there are no exact solutions available except approximations.