Quadratic spline collocation method for the time fractional subdiffusion equation

A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

“…[6][7][8]. In these models, the fractional diffusion equation (FDE) has been studied by many researchers, see [9][10][11][12][13][14][15][16][17][18] and references therein.…”

Numerical solution of fractional bioheat equation by quadratic spline collocation method

“…To avoid the singular matrix, the initial time collocation point τ 1 is replaced by an extra parameter θ ∈ (0, 1 2 ) in [16]. The contribution of the present paper is to extend the QSC method [16] to solve the fractional bioheat equation with mixed boundary value conditions for thermal therapy. This new introduced method does not need any extra parameter, and the obtained matrix is still nonsingular.…”

“…In these literatures, the studied models covering the QSC methods are mostly related to the integer order equations. Recently, Luo et al [16] exploited the QSC method to solve the time fractional subdiffusion equation with Dirichlet boundary value conditions, where the authors established a novel collocation method via taking the quadratic spline polynomials as basic functions, and found the proposed technique can enjoy the global error bound of O(τ 3 + h 3 ) and fourth-order accuracy at collocation points. To avoid the singular matrix, the initial time collocation point τ 1 is replaced by an extra parameter θ ∈ (0, 1 2 ) in [16].…”

“…Recently, Luo et al [16] exploited the QSC method to solve the time fractional subdiffusion equation with Dirichlet boundary value conditions, where the authors established a novel collocation method via taking the quadratic spline polynomials as basic functions, and found the proposed technique can enjoy the global error bound of O(τ 3 + h 3 ) and fourth-order accuracy at collocation points. To avoid the singular matrix, the initial time collocation point τ 1 is replaced by an extra parameter θ ∈ (0, 1 2 ) in [16]. The contribution of the present paper is to extend the QSC method [16] to solve the fractional bioheat equation with mixed boundary value conditions for thermal therapy.…”

Discrete septic spline quasi-interpolants for solving generalized Fredholm integral equation of the second kind via three degenerate kernel methods

“…The aim of [23] is to numerically solve the time fractional subdiffusion equation with Dirichelt boundary value conditions by use of the collocation method based on quadratic spline. In the paper, the authors explore, in details, the co-efficient matrix of the discretized linear system.…”