A numerical method for a partial integro-differential equation
SIAM Journal on Numerical Analysis
A difference scheme for a nonlinear partial integrodifferential equation
SIAM Journal on Numerical Analysis
A finite difference scheme for partial integro-differential equations with a weakly singular kernel
Applied Numerical Mathematics
The Wright functions as solutions of the time-fractional diffusion equation
Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Numerical simulations of 2D fractional subdiffusion problems
Journal of Computational Physics
A compact finite difference scheme for the fractional sub-diffusion equations
Journal of Computational Physics
A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
Journal of Computational Physics
Error Estimates of Crank-Nicolson-Type Difference Schemes for the Subdiffusion Equation
SIAM Journal on Numerical Analysis
Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions
Journal of Computational Physics
Data regularization for a backward time-fractional diffusion problem
Computers & Mathematics with Applications
Applied Numerical Mathematics
Journal of Scientific Computing
A high-order compact exponential scheme for the fractional convection-diffusion equation
Journal of Computational and Applied Mathematics
Orthogonal spline collocation methods for the subdiffusion equation
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Exponentially accurate spectral and spectral element methods for fractional ODEs
Journal of Computational Physics
Journal of Computational Physics
Two finite difference schemes for time fractional diffusion-wave equation
Numerical Algorithms
Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation
Journal of Scientific Computing
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A fully discrete difference scheme is derived for a diffusion-wave system by introducing two new variables to transform the original equation into a low order system of equations. The solvability, stability and L"~ convergence are proved by the energy method. Similar results are provided for a slow diffusion system. A numerical example demonstrates the theoretical results.