Second order spline method for fractional Bagley-Torvik equation with variable coefficients and Robin boundary conditions
Publish place: Journal of Mathematical Modeling، Vol: 11، Issue: 1
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JMMO-11-1_008
تاریخ نمایه سازی: 19 خرداد 1403
Abstract:
A fractional Bagley-Torvik equation of variable coefficients with Robin boundary conditions is considered in this paper. We prove the existence of the solution which is demonstrated by converting the boundary value problem into a Volterra integral equation of the second kind and also prove the uniqueness of the solution by using the minimum principle. We propose a numerical method that combines the second order spline approximation for the Caputo derivative and the central difference scheme for the second order derivative term. Meanwhile, the Robin boundary conditions is approximated by three-point endpoint formula. It is to be proved that this method is of second order convergent. Numerical examples are provided to demonstrate the accuracy and efficiency of the method.
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Authors
Joe Christin Mary S
Department of Mathematics, Bharathidasan University, Tiruchirappalli - ۶۲۰ ۰۲۴, Tamilnadu, India
Ayyadurai Tamilselvan
Department of Mathematics, Bharathidasan University, Tiruchirappalli - ۶۲۰ ۰۲۴, Tamilnadu, India