Solving Diffusion Equation Using a New Multiquadric Quasi-interpolation

DOI

10.2991/csss-14.2014.76How to use a DOI?

Keywords

Multiquadric quasi-interpolation;diffusion equation; shape-preserving property; approximation capacity

Abstract

In this paper, a new univariate quasi-interpolation operator is presented by means of construction way with cubic Multiquadric functions. It possesses univariate cubic polynomial reproduction property, quasi convexity-preserving and shape-preserving of order 4 properties, and a higher convergence rate. First, the quasi-interpolation operator is applied to approximate the derivative of order and its approximation capacity is obtained, i.e., Second, it is used to construct numerical schemes to solve the diffusion equation. Using the derivative of the quasi-interpolation to approximate the spatial derivative of the differential equation. And applying Crank-Nicolson scheme and back Euler scheme to approximate the temporal derivative of the differential equation. And as , the computational accuracy of the scheme is both and respectively. Finally, some numerical examples is given to verify the scheme for the one-dimensional diffusion equation. The numerical results show that the numerical solution are very close to the exact solution.

Copyright

© 2014, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Cao Junying
AU  - Wang Ziqiang
PY  - 2014/06
DA  - 2014/06
TI  - Solving Diffusion Equation Using a New Multiquadric Quasi-interpolation
BT  - Proceedings of the 3rd International Conference on Computer Science and Service System
PB  - Atlantis Press
SP  - 324
EP  - 327
SN  - 1951-6851
UR  - https://doi.org/10.2991/csss-14.2014.76
DO  - 10.2991/csss-14.2014.76
ID  - Junying2014/06
ER  -