A new numerical scheme for third-order singularly Emden–Fowler equations using quintic B-spline function
Bin Lin
Abstract
In this paper, we investigate a numerical scheme for the singular Emden–Fowler problem using quintic B-spline. We eliminate the singularity of the problem according to Lopita's law and obtain a new high-precision solution through a linear combination of the original solutions. We theoretically analyse the stability, truncation errors and convergence of the scheme and also verify it through several numerical experiments. We also provide some numerical examples to prove the efficiency of this numerical scheme and compare it with some earlier work done.
Topics & Concepts
MathematicsQuintic functionSingularityApplied mathematicsNumerical analysisConvergence (economics)Spline (mechanical)Numerical stabilityScheme (mathematics)Mathematical analysisNonlinear systemEconomicsQuantum mechanicsPhysicsStructural engineeringEngineeringEconomic growthDifferential Equations and Numerical MethodsFractional Differential Equations SolutionsNonlinear Waves and Solitons