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Ordokhani, Yadollah, Derakhshan, Mohammad Hossein, Kumar, Pushpendra. (1404). A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES. سامانه مدیریت نشریات علمی, (), -. doi: 10.22034/cmde.2025.66080.3074
Yadollah Ordokhani; Mohammad Hossein Derakhshan; Pushpendra Kumar. "A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES". سامانه مدیریت نشریات علمی, , , 1404, -. doi: 10.22034/cmde.2025.66080.3074
Ordokhani, Yadollah, Derakhshan, Mohammad Hossein, Kumar, Pushpendra. (1404). 'A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES', سامانه مدیریت نشریات علمی, (), pp. -. doi: 10.22034/cmde.2025.66080.3074
Ordokhani, Yadollah, Derakhshan, Mohammad Hossein, Kumar, Pushpendra. A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES. سامانه مدیریت نشریات علمی, 1404; (): -. doi: 10.22034/cmde.2025.66080.3074

A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES

Computational Methods for Differential Equations
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 مرداد 1404    اصل مقاله (2.49 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.66080.3074
نویسندگان
Yadollah Ordokhani* 1؛ Mohammad Hossein Derakhshan1؛ Pushpendra Kumar2
1Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
2Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey.
چکیده
In this paper, we propose a hybrid and efficient numerical scheme with high accuracy to obtain approximate solutions of the two-dimensional time-space diffusion-wave model in terms of the RiemannLiouville and Riesz fractional derivatives. To discretise the presented model, two approaches are used in the directions of space and time. In the time direction, we use a second-order accurate difference numerical method and the weighted shifted Grunwald derivative approximation of second-order. The weighted shifted Gr¨unwald derivative approximation is used to estimate the Riemann–Liouville’s fractional operator. Also, in the space direction, the Galerkin spectral method based on the modified Jacobi functions is used. The study of convergence and stability analysis for the proposed numerical approach is presented. At the end, some numerical examples are given to show the effectiveness of the proposed numerical scheme. For all the examples, graphs are drawn, and numerical results are
reported in tables.
کلیدواژه‌ها
Diffusion-wave model؛ Weakly singular kernel؛ Riesz fractional opertaor؛ Galerkin spectral method؛ Stability and convergence
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