Quadratic<i>B</i>-spline collocation method for two-parameter singularly perturbed problem on exponentially graded mesh
Meenakshi Shivhare, P. Pramod Chakravarthy, Devendra Kumar
Abstract
In this article, we present a quadratic B-spline collocation method on an exponentially graded mesh for the solution of two-parameter singularly perturbed boundary value problems (TP-SPBVPs) whose solution exhibits twin boundary layers at both endpoints of the domain of consideration. The method is shown to be parameters uniformly convergent of order two. To verify the theoretical estimates and to show the better accuracy of the proposed method compared to the existing results, numerical experiments are presented for several test problems.
Topics & Concepts
MathematicsQuadratic equationCollocation methodBoundary value problemMathematical analysisCollocation (remote sensing)Exponential growthRate of convergenceSpline (mechanical)B-splineSingular perturbationApplied mathematicsDomain (mathematical analysis)GeometryOrdinary differential equationDifferential equationComputer scienceChannel (broadcasting)Structural engineeringComputer networkEngineeringMachine learningDifferential Equations and Numerical Methods