NEW APPROACH BASED ON COLLOCATION AND SHIFTED CHEBYSHEV POLYNOMIALS FOR A CLASS OF THREE-POINT SINGULAR BVPS

In the recent decades, variety of real-life problems arises in astrophysics have been mimic using the class of three-point singular boundary value problems (BVPs). Finding an effective and accurate approach for a class of three-point BVPs is still a difficult problem, though. The goal of this paper is to design a numerical strategy for approximating a class of three-point singular boundary value problems using the collocation technique and shifted Chebyshev polynomials. Utilizing shifted Chebyshev polynomials, the problem is reduced to a matrix form, which is then converted into a system of nonlinear algebraic equations by employing the collocation points. The key advantages of the new approach are (a) it is a straightforward mathematical formulation, which makes it effortless to code, and (b) it is easily adaptable to solve various classes of three-point singular boundary value problems. The convergence analysis is carried out to ensure the viability of the proposed scheme. Various examples are considered and tested in order to illustrate its applicability and efficiency. The results show excellent accuracy and efficiency compared to the other existing methods.