Browsing by Author "Dwivedi, Kushal Dhar"

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Citation - WoS: 12
Citation - Scopus: 12
Numerical Solution of Highly Non-Linear Fractional Order Reaction Advection Diffusion Equation Using the Cubic B-Spline Collocation Method
(Walter de Gruyter Gmbh, 2022) Das, Subir; Rajeev; Baleanu, Dumitru; Dwivedi, Kushal Dhar
In this article, the approximate solution of the fractional-order reaction advection-diffusion equation with the prescribed initial and boundary conditions is found with the help of a cubic B-spline collocation method, which is unconditionally stable and convergent. The accuracy of the scheme is validated by applying the method on four existing problems having analytical solutions and through the evaluation of the absolute errors between numerical results and the exact solutions for different particular cases. Applying the proposed method on the last two numerical problems, it is shown that the method performs better than the existing methods even for very less number of spatial and temporal discretizations. The main contribution of the article is to develop an efficient method to solve the proposed fractional order nonlinear problem and to find the effect on solute concentration graphically due to increase in the non-linearity in the diffusion term for different particular values of parameters.
Numerical Solution of Nonlinear Space-Time Fractional-Order Advection-Reaction-Diffusion Equation
(2020) Dwivedi, Kushal Dhar; Rajeev; Das, Subir; Baleanu, Dumitru
In this article, a new algorithm is proposed to solve the nonlinear fractional-order one-dimensional solute transport system. The spectral collocation technique is considered with the Fibonacci polynomial as a basis function for the approximation. The Fibonacci polynomial is used to obtain derivative in terms of an operational matrix. The proposed algorithm is actually based on the fact that the terms of the considered problem are approximated through a series expansion of double Fibonacci polynomials and then collocated those on specific points, which provide a system of nonlinear algebraic equations which are solved by using Newton's method. To validate the precision of the proposed method, it is applied to solve three different problems having analytical solutions. The comparison of the results through error analysis is depicted through tables which clearly show the higher accuracy of order of convergence of the proposed method in less central processing unit (CPU) time. The salient feature of the article is the graphical exhibition of the movement of solute concentration for different particular cases due to the presence and absence of reaction term when the proposed scheme is applied to the considered nonlinear fractional-order space-time advection-reaction-diffusion model.