B-spline collocation methods and their convergence for a class of nonlinear derivative dependent singular boundary value problems

Pradip Roul and V.M.K. Prasad Goura

Applied Mathematics and Computation, 2019, vol. 341, issue C, 428-450

Abstract: This paper is concerned with the construction and convergence analysis of two B-spline collocation methods for a class of nonlinear derivative dependent singular boundary value problems (DDSBVP). The first method is based on uniform mesh, while the second method is based on non-uniform mesh. For the second method, we use a grading function to construct the non-uniform grid. We prove that the method based on uniform mesh is of second-order accuracy and the method based on non-uniform mesh is of fourth-order accuracy. Three nonlinear examples with derivative dependent source functions are considered to verify the performance and theoretical rate of convergence of present methods. Moreover, we consider some special cases of the problem under consideration in order to compare our methods with other existing methods. It is shown that our second method based on cubic B-spline basis functions has the same order of convergence as quartic B-spline collocation method [1]. Moreover, our methods yield more accurate results and are computationally attractive than the methods developed in [1–8]. The proposed methods are applied on three real-life problems, the first problem describes the distribution of radial stress on a rotationally shallow membrane cap, the second problem arises in the study of thermal explosion in cylindrical vessel and the third problem arises in astronomy.

Keywords: Derivative dependent source function; Uniform partition; Non-uniform partition; Convergence analysis; Shallow membrane cap; Thermal explosion (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318307835
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:341:y:2019:i:c:p:428-450

DOI: 10.1016/j.amc.2018.09.011

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().