A hybrid scheme for time fractional inverse parabolic problem

ABSTRACT

In order to solve the nonlinear time fractional inverse parabolic equations, two methods namely, combination of the finite difference method (FDM) and cubic B-spline collocation method are proposed. By using a sensor placed at a point inside the body and measuring the temperature at $x=x^{\ast }$, $0<x^{\ast }<1$, and applying the FDM to the inverse problem, a stable numerical solution to this problem is determined. Comparison of the approximate solution with the exact one shows that the used approach is simple and practical.

KEYWORDS:

• Time fractional Burgers equation
• finite difference method
• Cubic B-spline method
• collocation method
• inverse problems
• stable numerical solution
• noisy data

MSC 2010 NO.:

• 65M32
• 65M60

Disclosure statement

No potential conflict of interest was reported by the authors.