Numerical solution of the high thermal loss problem presented by a fractional differential equation

Abstract Three different numerical methods are used to solve singularly perturbed Able Volterra integral equation as presented by a fractional differential equation. Convergence and stability analysis together with the results of these methods are compared and contrasted when applied to the high thermal loss problem as an example of singularly perturbed Able Volterra integral equation.

[1]  A. H. Khater,et al.  Numerical solutions of integral and integro-differential equations using Legendre polynomials , 2007, Numerical Algorithms.

[2]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[3]  Singularly perturbed Volterra integral equations with weakly singular kernels , 2002 .

[4]  W. E. Olmstead,et al.  Singularly perturbed Volterra integral equations II , 1987 .

[5]  Peter Linz,et al.  Analytical and numerical methods for Volterra equations , 1985, SIAM studies in applied and numerical mathematics.

[6]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[7]  Alan D. Freed,et al.  Detailed Error Analysis for a Fractional Adams Method , 2004, Numerical Algorithms.

[8]  W. Olmstead,et al.  Singularly perturbed integral equations with endpoint boundary layers , 1989 .

[9]  Kai Diethelm,et al.  Generalized compound quadrature formulae for finite-part integrals , 1997 .

[10]  Hermann Brunner,et al.  Polynomial spline collocation methods for the nonlinear basset equation , 1989 .

[11]  I. Podlubny Fractional differential equations , 1998 .

[12]  H. Brunner,et al.  The numerical solution of Volterra equations , 1988 .

[13]  Z. Jackiewicz,et al.  Stability analysis of product θ-methods for Abel integral equations of the second kind , 1986 .

[14]  Charles G. Lange,et al.  Singular perturbation analysis of integral equations , 1988 .

[15]  G. Samuel Jordan,et al.  VOLTERRA INTEGRAL AND FUNCTIONAL EQUATIONS (Encyclopedia of Mathematics and its Applications 34) , 1991 .

[16]  J.-P. Kauthen,et al.  A survey of singularly perturbed Volterra equations , 1997 .

[17]  K. Diethelm MONOTONICITY RESULTS FOR A COMPOUND QUADRATURE METHOD FOR FINITE-PART INTEGRALS , 2004 .