A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition

Lu, Zhenhao; Fan, Wenping

doi:10.1007/s11075-024-01830-y

Numer Algor

2024

DOI: 10.1007/s11075-024-01830-y

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A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition

Zhenhao Lu,

Wenping Fan

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“…The fully discrete scheme's conditionally optimum error estimates are demonstrated. In reference [46], the fractional boundary conditions multi-term time-space diffusion equation is examined. The standard and shifted Grundwald Letnikov formula is used to approximate the fractional derivative in space, whereas the L 2 − 1 σ formula is used to estimate the fractional derivative in time.…”

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confidence: 99%

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Nawaz,

Arif,

Mansoor

et al. 2024

Fractal Fract

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An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme.

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mentioning

confidence: 99%

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Nawaz,

Arif,

Mansoor

et al. 2024

Fractal Fract

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A fast algorithm for multi-term time-space fractional diffusion equation with fractional boundary condition

Cited by 1 publication

References 31 publications

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

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