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Approximate calculation of the Caputo-type fractional derivative from inaccurate data. Dynamical approach
A specific formulation of the “classical” problem of mathematical analysis is considered. This is the problem of calculating the derivative of a...
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High-order algorithms for riesz derivative and their applications (IV)
The main goal of this article is to establish a new 4th-order numerical differential formula to approximate Riesz derivatives which is obtained by...
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Algebraic Fractional Order Differentiator Based on the Pseudo-State Space Representation
The aim of this paper is to design an algebraic fractional order differentiator for a class of commensurate fractional order linear systems modeled...
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Linear hybrid-variable methods for advection equations
We propose a general hybrid-variable (HV) framework to solve linear advection equations by utilizing both cell-average approximations and nodal...
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Fractional-Compact Numerical Algorithms for Riesz Spatial Fractional Reaction-Dispersion Equations
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost...
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Relations between directional derivatives for smooth functions in 2D and 3D spaces
In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are...
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An Accurate Space–Time Pseudospectral Method for Solving Nonlinear Multi-Dimensional Heat Transfer Problems
In this paper, we consider the numerical solution of the nonlinear one- and two-dimensional heat transfer problems subject to the given initial...
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Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting
A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical...
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A New Matrix Approach For Solving Second-Order Linear Matrix Partial Differential Equations
The basic aim of this article is to present a novel efficient matrix approach for solving the second-order linear matrix partial differential...
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Conceptual design of a selectable fractional-order differentiator for industrial applications
In the past decade, researchers working on fractional-order systems modeling and control have been considering working on the design and development...
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A computational tool for comparing all linear PDE solvers
The paper provides a computational technique that allows to compare all linear methods for PDE solving that use the same input data. This is done by...
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Order-preserving derivative approximation with periodic radial basis functions
In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis...
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Fractional integration toolbox
The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets....
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Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u ( x 1 , x 2 ) at the vertices...
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Matrix method for numerical solution of space-time fractional diffusion-wave equations with three space variables
In the present paper we solve space-time fractional diffusion-wave equations with three space variables, using matrix method. Here, in particular we...
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Extremum of second-order directional derivatives
In this paper, the extremum of second-order directional derivatives, i.e. the gradient of first-order derivatives is discussed. Given second-order...
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Generator, multiquadric generator, quasi-interpolation and multiquadric quasi-interpolation
The aim of this survey paper is to propose a new concept “generator”. In fact, generator is a single function that can generate the basis as well as...
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Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates
This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling...