On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Abstract

The exact solution is calculated for fractional telegraph partial differential equation depend on initial boundary value problem. Stability estimates are obtained for this equation. Crank-Nicholson difference schemes are constructed for this problem. The stability of difference schemes for this problem is presented. This technique has been applied to deal with fractional telegraph differential equation defined by Caputo fractional derivative for fractional orders α = 1.1, 1.5, 1.9. Numerical results confirm the accuracy and effectiveness of the technique.

Numerical investigations of a new singular second-order nonlinear coupled functional Lane–Emden model

“…The present investigations show that the spectral collocation method is an effective and suitable scheme for solving the nonlinear LE second-order system of FD equations. In the future, the designed method is an alternate promising solver to be exploited to examine the computational models of fluid dynamics, wire coating model, thin-film flow, squeezing flow systems, Jeffery Hamel type of systems, stretching flow problems, calendaring models, food processing systems, and related research areas [50][51][52][53][54] 2.23 10 −9 × 2.59 10 −9 × 6.10 10 −9 × 8.50 10 −9 × 4.55 10 −9 × 7.78 10 −9 × Figure 7: E convergence of Problem III. Funding: The first author is partially supported by Ministerio de Ciencia, Innovación y Universidades grant number PGC2018-097198-B-I00 and Fundación Séneca de la Región de Murcia grant number 20783/PI/18.…”

A Neuro-Swarming Intelligence-Based Computing for Second Order Singular Periodic Non-linear Boundary Value Problems

“…Statistical interpretation of findings through performance indices of TIC, EVAF, and ENSE based on 60 executions/trials of the solver for obtaining the solution of singular periodic non-linear model validate the trustworthiness, accurateness and robustness. Moreover, the values of the mean, median and semi interquartile range tabulated in Tables 1, 2 provide the precise and accurate values of the presented scheme ANN-PSO-IPS. In future, the designed approach is a promising alternate solver to be exploited/explored to investigate the computational fluid dynamics problems, especially thin film flow, wire coating analysis, squeezing flow models, Jeffery Hamel flow, calendaring problems, stretching flow problems, food processing models, and related fields [57][58][59][60][61][62].…”

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

“…Jonathan Lenells provided foundation for the geometric study of HS equation, this exhibits a geodesic flow. The system of nonlinear DEs like Hunter-Saxton, Camassa-Holm and Degasperis-Procesi was analyzed by variational principle to find the weak solutions in [8] , Volterra-Fredholm integral equations [9] , Boussinesq equations [10] , Schrödinger equation [11] , [12] , telegraph PDEs [13] , [14] , Burgers equation [15] . There are several researches in the literature, that are examined by the different techniques [16] , [17] , [18] , [19] , [20] .…”