Unconditionally stable modified methods for the solution of two‐ and three‐dimensional telegraphic equation with Robin boundary conditions

Singh, Swarn; Singh, Suruchi; Lin, Ping; Arora, R

doi:10.1002/num.22299

Cited by 2 publications

(5 citation statements)

References 17 publications

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“…The section concerns with the implementation of the proposed LFSM ( 28)- (29), SDM (32)- (33) and FNM ( 34)- (36) to explore the numerical solution of time fractional telegraph equation in three dimensions [20,21,[24][25][26][27][28][29][30][31][32]. We also demonstrated our inclusive analysis to validate the strength of proposed computational methods by simulating all cases of time-fractional telegraph model against different parameters.…”

Section: Numerical Implementation With Discussionmentioning

confidence: 99%

“…x I 𝛼 is M y M z × M y M z order identity matrix. Elements in the matrix 2 A x can be computed using relation (21). Matrices 3 Ãy and 3 P𝛽 y are of same order M y M z × M y M z whose elements must satisfied the following relations.…”

Section: Lemmamentioning

confidence: 99%

“…In recent years, investigation of the solutions of three‐dimensional telegraph equation becomes the emerging research topic due to its enormous application in science and technology including electrical signal traveling along a transmission cable [16] random walk of animals [17] clinical diagnosis [18] and vibration of structures [19]. In this work, we discussed the following three‐dimensional time‐fractional nonlinear telegraph equation in three‐dimensions which is defined in the domain Ω = { x = ( x , y , z ), 0 ≤ x , y , z ≤ 1} and 0 ≤ t ≤ T as [17, 20, 21],

\begin{array}{c} ((), _{0}^{C} D_{t}^{2 α} + μ_{1} ((), boldx, t)_{0}^{C} D_{t}^{α} + μ_{2} ((), boldx, t)) u ((), boldx, t) \\ = ([], μ_{3} ((), boldx, t) \frac{\partial^{2}}{\partial x^{2}} + μ_{4} ((), boldx, t) \frac{\partial^{2}}{\partial y^{2}} + μ_{5} ((), boldx, t) \frac{\partial^{2}}{\partial z^{2}}) u ((), boldx, t) + F ((), u) + ϕ ((), boldx, t), \end{array}

along with the following initial and Dirichlet boundary conditions.

u (x, 0) = f_{1} (boldx), u_{t} (x, 0) = f_{2} (boldx) where x = (x, y, z) \in Ω

u (x, t) = g ()

…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, investigation of the solutions of three-dimensional telegraph equation becomes the emerging research topic due to its enormous application in science and technology including electrical signal traveling along a transmission cable [16] random walk of animals [17] clinical diagnosis [18] and vibration of structures [19]. In this work, we discussed the following three-dimensional time-fractional nonlinear telegraph equation in three-dimensions which is defined in the domain Ω = {x = (x, y, z), FIGURE 1 Computation domain and mesh distribution for Burger's equations 0 ≤ x, y, z ≤ 1} and 0 ≤ t ≤ T as [17,20,21],…”

mentioning

confidence: 99%

“…They considered five test problems to show the efficiency and reliability of the proposed method. An unconditionally stable modified three-level implicit difference methods having order two in time and four in space developed by Singh et al [21] for the numerical solutions of telegraph equation in multidimensional space. Ming and Ali [20] discussed a detailed study of numerical solution of three-dimensional telegraph equation via a novel group iterative schemes.…”

mentioning

confidence: 99%

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