A novel quintic B-spline technique for numerical solution of fourth-order singularly-perturbed boundary value problems with discontinuous source terms

The current research proposes a novel efficient quintic B-spline (QBS) numerical technique based on piecewise uniform mesh for the numerical solution of fourth-order singularly perturbed boundary value problems (SPBVP) with discontinuous source terms (DST). The fifth-degree basis spline functions are employed along with a new approximation for the fourth-order derivative without altering the order of differential equations in which they appear. The proposed method is verified based on two problems to corroborate the scheme. The comparison of computational results shows that the proposed approach outperforms the existing approach in the literature. The stability and truncation error of the proposed way is analyzed.