High‐order schemes and their error analysis for generalized variable coefficients fractional reaction–diffusion equations

DOI10.1002/mma.9458OpenAlexW4380787539MaRDI QIDQ6179564

Jesus Vigo Aguiar, Anshima Singh, Sunil Kumar

Publication date: 16 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.9458

zbMATH Keywords

reaction-diffusion equationhigh ordergeneralized fractional derivativeparametric quintic spline\(gL2 - 1_{\sigma}\) formula

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
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• Numerical and analytical solutions of new generalized fractional diffusion equation
• An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations
• A compact finite difference scheme for the fractional sub-diffusion equations
• Parametric spline functions for the solution of the one time fractional Burgers equation
• Parametric quintic-spline approach to the solution of a system of fourth-order boundary-value problems
• Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation
• Compact finite difference method for the fractional diffusion equation
• A high order B-spline collocation method for linear boundary value problems
• Fractals and fractional calculus in continuum mechanics
• Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations
• A higher order non-polynomial spline method for fractional sub-diffusion problems
• New compact difference scheme for solving the fourth-order time fractional sub-diffusion equation of the distributed order
• Quintic B-spline collocation method for second order mixed boundary value problem
• The role of fractional calculus in modeling biological phenomena: a review
• Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems
• High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
• A fractional derivative with two singular kernels and application to a heat conduction problem
• A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative
• Chaotic behaviour of fractional predator-prey dynamical system
• The effect of market confidence on a financial system from the perspective of fractional calculus: numerical investigation and circuit realization
• An efficient numerical technique for solving nonlinear singularly perturbed reaction diffusion problem
• Analysis and some applications of a regularized \(\Psi\)-Hilfer fractional derivative
• A gWSGL numerical scheme for generalized fractional sub-diffusion problems
• Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment
• Some generalized fractional calculus operators and their applications in integral equations
• Numerical solutions and analysis of diffusion for new generalized fractional Burgers equation
• Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives
• High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay
• Generalized Alikhanov's approximation and numerical treatment of generalized fractional sub-diffusion equations
• A high order convergent numerical method for singularly perturbed time dependent problems using mesh equidistribution
• A convergent exponential B-spline collocation method for a time-fractional telegraph equation
• On fractional thermoelasticity
• Parametric quintic spline solution for sixth order two point boundary value problems
• Numerical solutions of fractional advection–diffusion equations with a kind of new generalized fractional derivative
• Error Estimate of Fourth-Order Compact Scheme for Linear Schrödinger Equations
• Higher order numerical approximation for time dependent singularly perturbed differential‐difference convection‐diffusion equations
• Parametric quintic spline solution of third-order boundary value problems
• Robust High Order Convergence of an Overlapping Schwarz Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems
• Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion problems
• Linear Fractional Diffusion-Wave Equation for Scientists and Engineers
• Advances in Fractional Calculus

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