The design of new high-order group iterative method in the solution of two-dimensional fractional cable equation
Muhammad Asim Khan, Norhashidah Hj. Mohd. Ali, Nur Nadiah Abd Hamid
Abstract
In this article, a new high-order explicit group iterative scheme is developed for the solution of the two-dimensional time fractional cable equation. The proposed scheme is derived from the Crank-Nicolson (C-N) high-order compact finite difference method, where the Caputo discretization and C-N high-order approximations are used for the time fractional and space derivative respectively. The stability and convergence of the proposed scheme are also established. Finally, two numerical examples are presented to show the accuracy and efficiency of the scheme.
Topics & Concepts
DiscretizationMathematicsConvergence (economics)Stability (learning theory)Order (exchange)Scheme (mathematics)Group (periodic table)Fractional calculusApplied mathematicsDerivative (finance)Iterative methodCable theorySpace (punctuation)Mathematical analysisMathematical optimizationComputer sciencePhysicsTelecommunicationsFinanceCable harnessCable glandFinancial economicsMachine learningQuantum mechanicsEconomicsEconomic growthOperating systemFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods in engineering