On a collocation method for the time-fractional convection-diffusion equation with variable coefficients
For researchers solving fractional partial differential equations, this work presents an incremental hybrid method that combines existing techniques without clear evidence of superiority over existing approaches.
The paper proposes a new collocation method combining sine-cosine wavelet operational matrices and exponential B-spline interpolation to solve the time-fractional convection-diffusion equation with variable coefficients. Numerical tests demonstrate the method's validity and applicability, but no concrete performance numbers are provided.
In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients. The operational matrix of fractional order integration is first derived based on sine-cosine wavelet functions, which helps to convert the underlying equation into a linear algebraic system. Then, an exponential B-spline method is introduced in spatial direction. On selecting a set of proper collocation points, the method in presence is evaluated on several test problems and the numerical results finally illustrate its validity and applicability.