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Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method

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Mathematical Analysis and its Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 143))

Abstract

In this article, a modified cubic B-spline differential quadrature method (MCB-DQM) is proposed to solve some of the basic differential equations. Here we have considered an ordinary differential equation of order two along with heat equation and one- and two-dimensional wave equations. A nonlinear ordinary differential equation of order two is also considered. The ordinary differential equation is reduced to a system of nonhomogeneous linear equations which is then solved by using the Gauss elimination method, whereas the heat equation and the one-dimensional and two-dimensional heat and wave equations are reduced to a system of ordinary differential equations. The system is then solved by the optimal four-stage three-order strong stability preserving time stepping Runge–Kutta (SSP-RK43) scheme. The reliability and efficiency of the method have been tested on six examples.

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Authors and Affiliations

  1. Department of Mathematics, IIT Roorkee, Roorkee, 247667, Uttarakhand, India

    R. C. Mittal & Sumita Dahiya

Authors
  1. R. C. Mittal
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  2. Sumita Dahiya
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Corresponding author

Correspondence to Sumita Dahiya .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    R. N. Mohapatra

  3. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Uaday Singh

  4. Dept. of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

    H. M. Srivastava

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Mittal, R.C., Dahiya, S. (2015). Numerical Solutions of Differential Equations Using Modified B-spline Differential Quadrature Method. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_42

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