A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces
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Publication:1874213
DOI10.1016/S0168-9274(02)00186-1zbMath1023.65151OpenAlexW2046976085MaRDI QIDQ1874213
César Palencia, Eduardo Cuesta
Publication date: 22 May 2003
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0168-9274(02)00186-1
stabilityconvergenceBanach spacesnumerical examplesintegro-differential equationerror expressionfractional trapezoidal rule
Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Abstract integral equations, integral equations in abstract spaces (45N05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convolution quadrature and discretized operational calculus. I
- Integrodifferential equation which interpolates the heat equation and the wave equation. II
- On convolution quadrature and Hille-Phillips operational calculus
- A finite difference scheme for partial integro-differential equations with a weakly singular kernel
- Discretization with variable time steps of an evolution equation with a positive-type memory term
- Discretized Fractional Calculus
- A Stability Result for Sectorial Operators in Banach Bpaces
- Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
- Time Discretization of an Integro-Differential Equation of Parabolic Type
- A Numerical Method for a Partial Integro-Differential Equation
- A note on collocation methods for Volterra integro-differential equations with weakly singular kernels
- Fractional Calculus
- Numerical solution of an evolution equation with a positive-type memory term
- Long-Time Numerical Solution of a Parabolic Equation with Memory
- Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term