A formally second‐order <scp>backward differentiation formula</scp> Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential transformation
DOI10.1002/num.22703OpenAlexW3112464302MaRDI QIDQ6067410
Publication date: 14 December 2023
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.22703
Volterra integro-differential equationsinc-collocation methoddouble exponential transformationstability and convergence analysissecond-order convolution quadrature rule
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Volterra integral equations (45D05) Fractional partial differential equations (35R11)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Double exponential transformation in the sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation
- On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel. I: Smooth initial data
- On the discretization in time for a parabolic integrodifferential equation with a weakly singular kernel. II: Nonsmooth initial data
- Convolution quadrature and discretized operational calculus. I
- The global behavior of time discretization for an abstract Volterra equation in Hilbert space
- Optimality of the double exponential formula -- functional analysis approach
- Compact alternating direction implicit scheme for integro-differential equations of parabolic type
- BDF ADI orthogonal spline collocation scheme for the fractional integro-differential equation with two weakly singular kernels
- A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model
- An efficient spline collocation method for a nonlinear fourth-order reaction subdiffusion equation
- Numerical solution of variable-order fractional integro-partial differential equations via sinc collocation method based on single and double exponential transformations
- The Crank-Nicolson-type sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel
- A second order BDF alternating direction implicit difference scheme for the two-dimensional fractional evolution equation
- Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the sinc-collocation method based on the double exponential transformation
- The double exponential sinc collocation method for singular Sturm-Liouville problems
- A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel
- Discretized Fractional Calculus
- Function classes for successful DE-Sinc approximations
- A second-order accurate numerical method for a semilinear integro-differential equation with a weakly singular kernel
- Bifurcation with Memory
- A Numerical Method for a Partial Integro-Differential Equation
- Finite element methods for parabolic and hyperbolic partial integro-differential equations
- The Sinc-Galerkin Method for Fourth-Order Differential Equations
- Finite Element Approximation of a Parabolic Integro-Differential Equation with a Weakly Singular Kernel
- A "Sinc-Galerkin" Method of Solution of Boundary Value Problems
- Numerical solution of an evolution equation with a positive-type memory term
- Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method
- Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
- Near optimality of the sinc approximation
- A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels
- On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
- Analysis of adaptive BDF2 scheme for diffusion equations
- Unconditional convergence of linearized orthogonal spline collocation algorithm for semilinear subdiffusion equation with nonsmooth solution
