A local meshless method to approximate the time-fractional telegraph equation

Kumar, Alpesh; Bhardwaj, Akanksha; Dubey, Shruti

doi:10.1007/s00366-020-01006-x

Cited by 29 publications

(16 citation statements)

References 57 publications

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“…Problem 4.1. [3,16,17] Consider the time fractional TDE having non-polynomial exact solution…”

Section: Numerical Problemsmentioning

confidence: 99%

“…From Figure 1, this solution takes five decimal accuracies (10 −5 ). Besides, Table 1 compares the computation results of E RM S in terms of the proposed (PM), the local meshless (LMM) [16], the radial basis function (RBF) [3] and the reproducing kernel (RKM) [17] methods. It can be noticed from Table 1 that the proposed method achieves far more accurate approximation than the other methods with respect to the low computation limit (N) and each specified fractional derivative.…”

Section: Numerical Problemsmentioning

confidence: 99%

“…On the other hand, the telegraph differential equations (TDEs) can be appeared differently in the study of the wave propagation theory on the behaviour of electrical signals found in a cable transmission system [12,13], particle transport applications [14] and Brownian motion processes [15]. As a fractional sense of TEs, some numerical studies can be detailed as follows: Kumar et al [16] have studied a local meshless method to acquire the solutions of time fractional TDEs with one and two dimensional forms. Hosseini et al [3] have deployed the radial basis function method for time fractional TDEs.…”

Section: Introductionmentioning

confidence: 99%

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A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Kürkçü

2021

MANAS Journal of Engineering

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This paper is concerned with solving numerically the time fractional telegraph equations having multiple space and time delays by proposing a novel matrix-collocation method dependent on the Delannoy polynomial. This method enables easy and fast approximation tool consisting of the matrix expansions of the functions using only the Delannoy polynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, the residual error computation, which involves the same procedure as the method, provides the improvement of the solutions. The method is evaluated under some valuable error tests in the numerical applications. To do this, a unique computer module is devised. The present results are compared with those of the existing methods in the literature, in order to oversee the precision and efficiency of the method. One can express that the proposed method admits very consistent approximation for the equations in question.

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“…Problem 4.1. [3,16,17] Consider the time fractional TDE having non-polynomial exact solution…”

Section: Numerical Problemsmentioning

confidence: 99%

Section: Numerical Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Kürkçü

2021

MANAS Journal of Engineering

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“…Meshfree techniques 33‐41 are very interesting and impressive for solving PDEs since these methods include simple projecting, variety in solving metamorphosis, and have capability to improve non‐smooth solutions. The meshless local Petrov–Galerkin (MLPG) method is an efficient meshfree method to solve PDEs with complicated domains.…”

Section: Introductionmentioning

confidence: 99%

“…Yin et al 30 applied a class of shifted high-order numerical schemes for the fractional mobile/immobile transport equations. For other numerical methods to solving this models, see Zhao et al 31 and Wang et al 32 Meshfree techniques [33][34][35][36][37][38][39][40][41] are very interesting and impressive for solving PDEs since these methods include simple projecting, variety in solving metamorphosis, and have capability to improve non-smooth solutions. The meshless local Petrov-Galerkin (MLPG) method is an efficient meshfree method to solve PDEs with complicated domains.…”

Section: Introductionmentioning

confidence: 99%

An efficient meshless method based on the moving Kriging interpolation for two‐dimensional variable‐order time fractional mobile/immobile advection‐diffusion model

Habibirad

Hesameddini

Heydari

et al. 2020

Math Methods in App Sciences

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In this work, we introduce an efficient meshless technique for solving the two‐dimensional variable‐order time‐fractional mobile/immobile advection‐diffusion model with Dirichlet boundary conditions. The main advantage of this scheme is to obtain a global approximation for this problem which reduces such problems to a system of algebraic equations. To approximate the first and fractional variable‐order against the time, we use the finite difference relations. The proposed method is based on the moving Kriging (MK) interpolation shape functions. To discretize this model in space variables, we use the MK interpolation. Duo to the fact that the shape functions of MK have Kronecker's delta property, boundary conditions are imposed directly and easily. To illustrate the capability of the proposed technique on regular and irregular domains, several examples are presented in different kinds of domains and with uniform and nonuniform nodes. Also, we use this scheme to simulating anomalous contaminant diffusion in underground reservoirs.

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Efficient numerical algorithms of time fractional telegraph‐type equations involving Hadamard derivatives

Cen

Wang

2022

Math Methods in App Sciences

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In this paper, we study the finite difference/iterative method for the fractional telegraph equation with Hadamard derivatives. The model is first transformed into an equivalent fractional integro‐differential equation, then the technic of exponential type meshes is adopted. The resulting discrete coefficients of Hadamard fractional integral own several graceful properties, which are crucial in numerical analysis. To conquer the difficulty caused by weak regularity, we also propose iterative schemes. The error estimate is equal to O()false(logtfalse)n+γ,0.1em1

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A local meshless method to approximate the time-fractional telegraph equation

Cited by 29 publications

References 57 publications

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

An efficient meshless method based on the moving Kriging interpolation for two‐dimensional variable‐order time fractional mobile/immobile advection‐diffusion model

Efficient numerical algorithms of time fractional telegraph‐type equations involving Hadamard derivatives

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