Numerical Simulations of Third-Order Singularly Perturbed Boundary Value Problems

This paper introduces a quartic trigonometric B-spline (QTBS) for the purpose of producing numerical solutions for a third-order singularly perturbed boundary value problem (SpBvp) characterized by the presence of a minuscule parameter multiplying the highest-order derivative. The QTBS basis function, denoted as \(T_{i}(x)\) , is applied at various nodal points. This approach is employed subsequent to the modification of the problem at the singularity point through the utilization of the L’Hopital rule. Resulting system of equations is solved by Mathematica to get the solution. These present numerical results are compared with the numerical results that exist in the literature like the method presented by Mishra (Am J Numer Anal 3(1):18–24, 2015) [1]. This demonstrates that the approximate solutions produced by the numerical algorithm developed using the QTBS are better than the regular quartic B-spline (QBS).