Numerical solution of fractional advection-diffusion equation with a nonlinear source term. (English) Zbl 1319.35290
The paper analyzes a special kind of fractional advection-diffusion equation with a nonlinear source term. Stability and convergence are studied and numerical examples are discussed.
Reviewer: Răzvan Răducanu (Iaşi)
MSC:
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
fractional advection-diffusion equation; Riemann-Louville derivative; Jacobi polynomials; operational matrix; collocation method; stability analysis and convergenceReferences:
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