Numerical solution of time-fractional telegraph equation by using a new class of orthogonal polynomials

‎In this article‎, ‎an efficient numerical method based on a new class of orthogonal polynomials‎, ‎namely Chelyshkov polynomials‎, ‎has been presented to approximate solution of time-fractional telegraph (TFT) equations‎. ‎The fractional operational matrix of the Chelyshkov polynomials along with the typical collocation method is used to reduces TFT equations to a system of algebraic equations‎. ‎The error analysis of the proposed collocation method is also investigated‎. ‎A comparison with other published results confirms that the presented Chelyshkov collocation approach is efficient and accurate for solving TFT equations‎. ‎Illustrative examples are included to demonstrate the efficiency of the Chelyshkov method‎.

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity

The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the aforementioned differential equations. Moreover, an error bound of the present approach by using the maximum norm was computed and an error estimation technique based on the residual function is presented. Finally, the validity and applicability of the presented collocation scheme are shown via four numerical test examples.

Numerical and analytical investigation for solutions of fractional Oskolkov–Benjamin–Bona–Mahony–Burgers equation describing propagation of long surface waves

In this paper, a novel meshless numerical scheme to solve the time-fractional Oskolkov–Benjamin–Bona–Mahony–Burgers-type equation has been proposed. The proposed numerical scheme is based on finite difference and Kansa-radial basis function collocation approach. First, the finite difference scheme has been employed to discretize the time-fractional derivative and subsequently, the Kansa method is utilized to discretize the spatial derivatives. The stability and convergence analysis of the time-discretized numerical scheme are also elucidated in this paper. Moreover, the Kudryashov method has been utilized to acquire the soliton solutions for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme.

An adaptive wavelet collocation method for the optimal heat source problem

Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

Hyperbolic compartmental models for epidemic spread on networks with uncertain data: Application to the emergence of COVID-19 in Italy

The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources such as the amount of infectious individuals. In this paper, we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interactions of a population partitioned, from an epidemiological point of view, on the basis of an extended compartmental structure and divided into commuters, moving on a suburban scale, and non-commuters, acting on an urban scale. Through a diffusive rescaling, the model allows us to recover classical diffusion equations related to commuting dynamics. The numerical solution of the resulting multiscale hyperbolic system with uncertainty is then tackled using a stochastic collocation approach in combination with a finite volume Implicit–Explicit (IMEX) method. The ability of the model to correctly describe the spatial heterogeneity underlying the spread of an epidemic in a realistic city network is confirmed with a study of the outbreak of COVID-19 in Italy and its spread in the Lombardy Region.