Abstract
In this paper, we introduce a high order numerical approximation method for convection diffusion wave equations armed with a multiterm time fractional Caputo operator and a nonlinear fixed time delay. A temporal second-order scheme which is behaving linearly is derived and analyzed for the problem under consideration based on a combination of the formula of L2−1σ and the order reduction technique. By means of the discrete energy method, convergence and stability of the proposed compact difference scheme are estimated unconditionally. A numerical example is provided to illustrate the theoretical results.
Highlights
IntroductionFractional derivatives and integrals have recently gained high interest in many fields of science
Fractional derivatives and integrals have recently gained high interest in many fields of science.The ability of classifying and capturing the memory and hereditary properties of various materials and processes is an advantage of fractional derivatives over their integer counterparts, e.g., the modeling of anomalous diffusion by fractional differential equations gives more informative and interesting models [1]
For time-fractional differential equations, the memory feature implies that all previous information is needed to evaluate the time fractional derivative at the current time level
Summary
Fractional derivatives and integrals have recently gained high interest in many fields of science. A numerical solution for a class of time fractional diffusion equations with delay is proposed in [13] that is based on a smooth difference approximation of specific L1 type. In [17], the authors proposed a spectral τ-scheme to discretize the fractional diffusion equation with distributed-order fractional derivative in time and Dirichlet boundary conditions. Two classes of finite difference methods that are based on backward differential formula discretization in the temporal direction are proposed in [19] to efficiently solve the semilinear space fractional reaction–diffusion equation with time-delay. Higher order numerical schemes are extremely scarce and difficult in regard to the analysis and implementation for the variable coefficient multiterm time fractional convection-diffusion wave equation with delay. The paper ends with a numerical illustration and a conclusion
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