Browsing by Author "Haq, Sirajul"

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Citation Count: Ghafoor, Abdul...et al. (2021). "An efficient numerical algorithm for the study of time fractional Tricomi and Keldysh type equations", Engineering With Computers.
An efficient numerical algorithm for the study of time fractional Tricomi and Keldysh type equations
(2021) Ghafoor, Abdul; Haq, Sirajul; Rasool, Amir; Baleanu, Dumitru; 56389
This work addresses a hybrid scheme for the numerical solutions of time fractional Tricomi and Keldysh type equations. In proposed methodology, Haar wavelets are used for discretization in space while theta-weighted scheme coupled with second order finite differences and quadrature rule are employed for temporal discretization and fractional derivative respectively. Stability of the proposed scheme is described theoretically and validated computationally which is an essential chunk of the current work. Efficiency of the suggested scheme is endorsed through resolutions level and time step size. Goodness of the obtained solutions confirmed through computing error norms E-infinity, E-2 and matching with existing results in literature. Moreover, convergence rate is also checked for considered problems. Numerical simulations show good performance for both 1D and 2D test problems.
Citation Count: Ali, Ihteram...et al. (2021). "An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations", Advances in Difference Equations, Vol. 2021, No. 1.
An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations
(2021) Ali, Ihteram; Haq, Sirajul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, the temporal part is discretized by finite difference method together with theta-weighted scheme. Then, for the approximation of spatial part of unknown function and its spatial derivatives, we use a mixed approach based on Lucas and Fibonacci polynomials. With the help of these approximations, we transform the nonlinear partial differential equation to a system of algebraic equations, which can be easily handled. We test the performance of the method on the generalized Burgers-Huxley and Burgers-Fisher equations, and one- and two-dimensional coupled Burgers equations. To compare the efficiency and accuracy of the proposed scheme, we computed L-infinity, L-2, and root mean square (RMS) error norms. Computations validate that the proposed method produces better results than other numerical methods. We also discussed and confirmed the stability of the technique.