ZZ Fourth Order Compact BVM for the Equation of Lateral Heat Loss

Authors

  • Zain Ul Abadin Zafar
  • M.O. Ahmad
  • A. Pervaiz
  • Nazir Ahmad

Abstract

In this paper we combine the boundary value method (for discretizing the temporal variable) and finite difference scheme (for discretizing the spatial variables) to numerically solve the Equation of Lateral Heat Loss. This equation is also used in Probability, Stochastic processes and Brownian movements of gases. We first employ a fourth order compact scheme to discretize the spatial derivatives, and then a linear system of ordinary differential equations is obtained. Then we apply a fourth order scheme of boundary value method to approach this system. After this we use the central difference scheme for the temporal variables. Therefore, this scheme can achieve fourth order accuracy for spatial variables. For stability analysis we have used the Von Neumann Stability. Numerical results are presented to illustrate the accuracy and efficiency of this compact difference scheme, compared with finite difference scheme.

References

S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite - Hadamard Inequalities and Applications, RGMIA, Monographs.

S. S. Dragomir, J. E. Pečarić and L. E. Persson,Some inequalities of Hadamard type, Soochow J. Math. (Taiwan), 21 (1995), 335- 341.

S. S. Dragomir and R. P. Agarwal,Two inequalities for differentiable mappings and applications to special means of real numbers and trapezoidal formula, Appl. Math. Lett.,11(5) (1998), 91-95.

E.K. Godunova and V. I. Levin, Neravenstva dlja funkeii širokogo klassa, žaščego vypuklye, monotonnye i nekotorye drugie vidy funkii, Vyscislitel. Mat. i. Fiz. Mezvuzov. Sb. Nauc. Trudov, MGPI, Moskva, 1985, 138-142.

S. Hussain, M. I. Bhatti and M. Iqbal, Hadamard-Type inequalities for -convex functins-I, Punjab University Jour. Math., 41(2009), 51-60.

U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comp., 147 (2004), 137-146.

C. E. M. Pearce and J. E. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formula, Appl. Math. Lett., 13(2)(2000), 51-55.

M. Z. Sarikaya, E. Set and M. E. Özdemir, On some new inequalities of Hadamard type involving -convex functions, Acta Math. Univ. Comenianae, Vol.LXXIX, 2(2010),265-272.

M. Z. Sarikaya, A. Saglam and H. Yildirim, On some Hadamard-type inequalities for h-convex functions, Jour. Math. Ineq., 2(3) (2008), 335- 341.

S. Varošanec, on h-convexity, J. Math. Anal. Appl., 326 (2007), 303-311.

Downloads

Published

2016-06-22

Issue

Section

Polymer Engineering and Chemical Engineering, Materials Engineering, Physics, Chemistry, Mathematics