Abstract
A singular boundary value problem arises in the conduction of heat through a solid and having other important applications is solved using a novel spline method. The removal of the singularity is done before applying a cubic B-spline and then a B-spline with a free parameter. The numerical examples show that the results have a very close agreement with exact solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hoog, F.R., Weiss, R.: Difference methods for boundary value problems with a singularity of the first kind. SIAM J. Numer. Anal. 13, 775–813 (1976)
Roul, P., Goura, V.P., Agarwal, R.: A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions. Appl. Math. Comput. 350, 283–304 (2019)
Reddien, G.W.: Projection methods and singular two point boundary value problems. Numer. Math. 21, 193–205 (1973)
Wazwaz, A.M.: The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models. Commun. Nonlinear Sci. Numer. Simul. 16, 3881–3886 (2011)
Kumar, M., Singh, N.: Modified adomain decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems. Comput. Chem. Eng. 34, 1750–1760 (2010)
Roul, P.: A new mixed MADM-collocation approach for solving a class of Lane-Emden singular boundary value problems J. . Math. Chem. 57, 945–969 (2019)
Verma, A.K., Pandit, B., Agarwal, R.P.: On approximate stationary radial solutions for a class of boundary value problems arising in epitaxial growth theory. J. Appl. Comput. Mech. 6(4), 713–734 (2020)
Kumar, M., Gupta, Y.: Methods for solving singular boundary value problems using splines: a review. J. Appl. Math. Comput. 32, 265–278 (2010)
Gupta, Y., Kumar, M.: A computational approach for solution of singular boundary value problem with applications in human physiology. Natl. Acad. Sci. Lett. 35(3), 189–193 (2012)
Gupta, Y., Srivastava, P.K., Kumar, M.: Application of B-spline to numerical solution of a system of singularly perturbed boundary value problems. Math. Aeterna 1, 405–415 (2011)
Chaurasia, A., Gupta, Y., Srivastava, P.C.: Numerical scheme based on non-polynomial spline functions for the system of second order boundary value problems arising in various engineering applications. J. Appl. Comput. Mech. https://doi.org/10.22055/JACM.2020.32435.2012
Xu, G., Wang, G.: Extended cubic uniform B-spline and [alpha]-B-spline. Acta Autom. Sin. 34, 980–984 (2008)
Prenter, P.M.: Splines and Variational Methods. Wiley (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Gupta, S., Sharma, S. (2022). A Numerical Method for a Problem Occurring in Conduction of Heat Through a Solid and Other Applications. In: Rao, V.V., Kumaraswamy, A., Kalra, S., Saxena, A. (eds) Computational and Experimental Methods in Mechanical Engineering. Smart Innovation, Systems and Technologies, vol 239. Springer, Singapore. https://doi.org/10.1007/978-981-16-2857-3_21
Download citation
DOI: https://doi.org/10.1007/978-981-16-2857-3_21
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-2856-6
Online ISBN: 978-981-16-2857-3
eBook Packages: EngineeringEngineering (R0)