One-Dimensional Heat Equation Subject to Both Neumann and Dirichlet Initial Boundary Conditions and Used a Spline Collocation Method

6 pages•Published: June 12, 2017

Abstract

In this paper, one-dimensional heat equation subject to both Neumann and Dirichlet initial boundary conditions is presented and a Spline Collocation Method is utilized for solving the problem. Also, Spline provides continuous solution in contrast to finite difference method, which only provides discrete approximations. It is found that this method is a powerful mathematical tool and can be applied to large class of linear and nonlinear problem in different fields of science and technology. Numerical results obtained by the present method are in a good agreement with the analytical solutions available in the literature.

Keyphrases: dirichlet and neumann boundary conditions, heat conduction, partial differential equations, spline collocation method

In: Rajkumar Buyya, Rajiv Ranjan, Sumantra Dutta Roy, Mehul Raval, Mukesh Zaveri, Hiren Patel, Amit Ganatra, Darshak G. Thakore, Trupti A. Desai, Zankhana H. Shah, Narendra M. Patel, Mukesh E. Shimpi, Rajiv B. Gandhi, Jagdish M. Rathod, Bhargav C. Goradiya, Mehfuza S. Holia and Dharita K. Patel (editors). ICRISET2017. International Conference on Research and Innovations in Science, Engineering and Technology. Selected Papers in Computing, vol 2, pages 107-112.

Links:	https://easychair.org/publications/paper/8Mr
	https://doi.org/10.29007/w6lj

BibTeX entry

@inproceedings{ICRISET2017:One_Dimensional_Heat_Equation,
  author    = {Nilesh Patel and Jigisha Pandya},
  title     = {One-Dimensional Heat Equation Subject to Both Neumann and Dirichlet Initial Boundary Conditions and Used a  Spline Collocation Method},
  booktitle = {ICRISET2017. International Conference on Research and Innovations in Science, Engineering and Technology. Selected Papers in Computing},
  editor    = {Rajkumar Buyya and Rajiv Ranjan and Sumantra Dutta Roy and Mehul Raval and Mukesh Zaveri and Hiren Patel and Amit Ganatra and Darshak G. Thakore and Trupti A. Desai and Zankhana H. Shah and Narendra M. Patel and Mukesh E. Shimpi and Rajiv B. Gandhi and Jagdish M. Rathod and Bhargav C. Goradiya and Mehfuza S. Holia and Dharita K. Patel},
  series    = {Kalpa Publications in Computing},
  volume    = {2},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/8Mr},
  doi       = {10.29007/w6lj},
  pages     = {107-112},
  year      = {2017}}

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