A new high order space derivative discretization for 3D quasi-linear hyperbolic partial differential equations

Mohanty, R. K.; Singh, Suruchi; Singh, Swarn

doi:10.1016/j.amc.2014.01.064

Cited by 5 publications

(6 citation statements)

References 21 publications

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“…The parameters introduced in the process of proving the stability are obtained to be independent of the grid sizes whereas parameters introduced in methods discussed in Refs. , and depend on the grid sizes. Various numerical experiments are carried out to show the efficiency and accuracy of the proposed methods.…”

Section: Discussionmentioning

confidence: 99%

“…A Numerov type approximation [15] with accuracy of O(k 2 + k 2 h 2 + h 4 ) for the solution of (3.1.1) for l, m, n = 1(1)N − 1, 0 < j ≤ J may be written as ( 2…”

Section: Methodsmentioning

confidence: 99%

“…A Numerov type approximation with accuracy of O ( k 2 + k 2 h 2 + h 4 ) for the solution of for l , m , n = 1(1) N − 1, 0 < j ≤ J may be written as

\begin{array}{l} δ_{t}^{2} U_{l, m, n}^{j} + \sqrt{a} ((), 2 μ_{t} δ_{t}) U_{l, m, n}^{j} + \frac{\sqrt{a}}{12} ((), δ_{x}^{2} + δ_{y}^{2} + δ_{z}^{2}) ((), 2 μ_{t} δ_{t}) U_{l, m, n}^{j} + {bU}_{l, m, n}^{j} \\ + ((), \frac{b}{12} - p^{2}) ((), δ_{x}^{2} + δ_{y}^{2} + δ_{z}^{2}) U_{l, m, n}^{j} - \frac{p^{2}}{6} ((), δ_{x}^{2} δ_{y}^{2} + δ_{y}^{2} δ_{z}^{2} + δ_{z}^{2} δ_{x}^{2}) U_{l, m, n}^{j} \\ + \frac{1}{12} ((), δ_{x}^{2} + δ_{y}^{2} + δ_{z}^{2}) δ_{t}^{2} U_{l, m, n}^{j} \\ = \frac{k^{2}}{12} ((), f_{l + 1, m, n}^{j} + f_{l - 1, m, n}^{j} + f_{l, m + 1, n}^{j} + f_{l, m - 1, n}^{j} + f_{l, m, n + 1}^{j} + f_{l, m, n - 1}^{j} + 6 f_{l, m}^{j}) \\ + O ((), k^{}) \end{array}

…”

Section: Three‐dimensional Telegraphic Equationmentioning

confidence: 99%

“…Hence, solving telegraphic equation is of major interest. In recent past, several techniques [3][4][5][6][7][8][9][10][11][12][13][14][15][16] are discovered to solve telegraphic equation in one, two, and three dimensions. Dehghan and Mohebbi [3] proposed an implicit collocation method for the solution of two-dimensional linear hyperbolic equation with Dirichlet boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed methods are three level implicit difference methods which are based on Numerov type approximations proposed in Refs. and . We discuss in detail the stability of the proposed methods by matrix stability method for solving telegraphic equation with Neumann boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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

Singh

Lin

et al. 2018

Numerical Methods Partial

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In this article, we discuss modified three level implicit difference methods of order two in time and four in space for the numerical solution of two‐ and three‐dimensional telegraphic equation with Robin boundary conditions. Ghost points are introduced to obtain fourth‐order approximations for boundary conditions. Matrix stability analysis is carried out to prove stability of the method for telegraphic equations in two and three dimensions with Neumann boundary conditions. Numerical experiments are carried out and the results are found to be better when compared with the results obtained by other existing methods.

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Section: Discussionmentioning

confidence: 99%

“…A Numerov type approximation [15] with accuracy of O(k 2 + k 2 h 2 + h 4 ) for the solution of (3.1.1) for l, m, n = 1(1)N − 1, 0 < j ≤ J may be written as ( 2…”

Section: Methodsmentioning

confidence: 99%

“…A Numerov type approximation with accuracy of O ( k 2 + k 2 h 2 + h 4 ) for the solution of for l , m , n = 1(1) N − 1, 0 < j ≤ J may be written as