The Application of Quartic Trigonometric B-spline for Solving Second Order Singular Boundary Value Problems - Akram, Tayyaba; Abbas, Muhammad; Ismail, Ahmad Izani (Communications in Mathematics and Applications, 2018)
In this paper, a quartic trigonometric B-spline collocation approach is described and presented for the numerical solution of the second order singular boundary value problems. Several numerical examples are discussed to exhibit the feasibility and capability of the technique. The unknown coefficients \(C_{i}\), \(i=-4,-3,…,n-1\) are obtained through optimization. The maximum errors \((L_{∞})\) and norm errors \((L_{2})\) are also computed for different space size steps to assess the performance of the proposed technique. The rate of convergence is discussed numerically to be of fourth-order. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The comparison shows that the quartic trigonometric B-spline method is superior as it yields more accurate solutions.