An asymptotic numerical method for singularly perturbed third-order ordinary differential equations of convection-diffusion type

Spectral methods for some singularly perturbed third order ordinary differential equations

“…As mentioned in the introduction, the second order SPODEs have been extensively studied but only few results on higher order equations are reported in the literature. The obtained approximate numerical solution maintains a good accuracy in little computer time compared with other methods [21][22][23]. Importance of the spectral collocation methods with interface point can be seen from the respective tabular results.…”

“…The authors in [21,22] have considered problems P1-P2, respectively, and derived stability result, convergence and error estimates.…”

“…Therefore we introduce an appropriate interface point d ∈ R = [0, 1] and hence apply the collocation method I and the collocation method II in the two intervals R 1 = [0, d] and 1]. The methods are to be compared with that of Valarmathi and Ramanujam [21][22][23] for the above problems.…”

“…A good number of articles have been appearing in the past two to three decades on non-classical methods which cover mostly second order singularly perturbed R. S. Temsah (B) Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt e-mail: Eltemssah@yahoo.com boundary value problems (SPBVPs). But only a few authors have developed numerical methods for higher-order differential equations [3,4,[16][17][18][19][20][21][22][23][24]. Singularly perturbed higher-order problems are classified on the basis that how the order of the original differential equation is affected if one sets = 0.…”

“…By employing of an asymptotic numerical fitted mesh method, Valarmathi and Ramanujam [21] has considered third order SPODEs of reaction-diffusion type. Also Valarmathi and Ramanujam [22] have considered third order SPODEs of convection-diffusion type and applied an asymptotic numerical method. In this paper the linear third order SPODEs of reaction-diffusion and convection-diffusion types are considered and then non-linear equations.…”