An iterative approximate method of solving boundary value problems using dual Bernstein polynomials
This is an incremental contribution for researchers working on numerical solutions of differential equations, offering an alternative approach without clear advantages over existing methods.
The authors propose an iterative method using dual Bernstein polynomials and least squares approximation to solve linear and nonlinear boundary value problems of arbitrary order. Examples demonstrate the method's versatility, but no concrete performance numbers are provided.
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties of dual Bernstein polynomials which guarantee high efficiency of our approach. The method can deal with both linear and nonlinear differential equations. Moreover, not only second order differential equations can be solved but also higher order differential equations. Illustrative examples confirm the versatility of our method.