COMPACT FINITE DIFFERENCES METHOD AND CAPUTO FRACTIONAL DERIVATIVE DEFINITION FOR LINEAR FRACTIONAL SCHRÖDINGER EQUATIONS
DOI10.17654/NM017010019zbMath1427.65159MaRDI QIDQ5204785
Nazan Caglar, Hikmet Caglar, Neslihan Er
Publication date: 5 December 2019
Published in: International Journal of Numerical Methods and Applications (Search for Journal in Brave)
dispersion analysisCaputo fractional derivative definitioncompact finite differences methodhomogeneous linear fractional Schrödinger equationnon-homogeneous linear fractional Schrödinger equation
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) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- A 6th order staggered compact finite difference method for the incompressible Navier-Stokes and scalar transport equations
- High-order compact implicit difference methods for parabolic equations in geodynamo simulation
- A compact finite difference scheme for the fractional sub-diffusion equations
- A note on boundary value problems for a coupled system of fractional differential equations
- Implicit compact difference schemes for the fractional cable equation
- Compact finite difference methods for high order integro-differential equations
- The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
- Analysis of material interface dicontinuities and superconvergent fluxes in finite difference theory
- Compact high-order schemes for the Euler equations
- Compact finite difference schemes with spectral-like resolution
- Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
- Higher order monotonic convective difference schemes
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Fractional quantum mechanics and Lévy path integrals
- Compact finite difference method for American option pricing
- Differential equations of fractional order:methods results and problem —I
- Differential-equation-based representation of truncation errors for accurate numerical simulation
- Nodal Superconvergence and Solution Enhancement for a Class of Finite-Element and Finite-Difference Methods
- Superconvergent derivatives: A Taylor series analysis
- Compact finite difference schemes on non-uniform meshes. Application to direct numerical simulations of compressible flows
- Compact high‐order finite‐element method for elliptic transport problems with variable coefficients
- Time fractional Schrödinger equation
- High-order compact scheme for boundary points
