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Volume 9, Issue 1
An Unconditionally Stable Numerical Method for Two-Dimensional Hyperbolic Equations

Swarn Singh, Suruchi Singh & Rajni Arora

DOI: 10.4208/eajam.280118.100518

East Asian J. Appl. Math., 9 (2019), pp. 195-211.

Published online: 2019-01

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  • Abstract

A collocation method based on exponential B-splines for two-dimensional second-order non-linear hyperbolic equations is studied. The initial equation is split into a system of coupled equations, each of which is transformed into a system of ordinary differential equations. The corresponding differential equations are solved by SSP-RK(2,2) method. It is shown that the method under consideration is unconditionally stable. Numerical experiments demonstrate its efficiency and accuracy.

  • Keywords

Collocation method, SSP-RK(2, 2), telegraph equation, tri-diagonal solver, unconditional stability.

  • AMS Subject Headings

65M60, 65M06, 65N30, 65N06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-195, author = {Swarn Singh, Suruchi Singh and Rajni Arora}, title = {An Unconditionally Stable Numerical Method for Two-Dimensional Hyperbolic Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {195--211}, abstract = {

A collocation method based on exponential B-splines for two-dimensional second-order non-linear hyperbolic equations is studied. The initial equation is split into a system of coupled equations, each of which is transformed into a system of ordinary differential equations. The corresponding differential equations are solved by SSP-RK(2,2) method. It is shown that the method under consideration is unconditionally stable. Numerical experiments demonstrate its efficiency and accuracy.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280118.100518 }, url = {http://global-sci.org/intro/article_detail/eajam/12942.html} }
TY - JOUR T1 - An Unconditionally Stable Numerical Method for Two-Dimensional Hyperbolic Equations AU - Swarn Singh, Suruchi Singh & Rajni Arora JO - East Asian Journal on Applied Mathematics VL - 1 SP - 195 EP - 211 PY - 2019 DA - 2019/01 SN - 9 DO - http://doi.org/10.4208/eajam.280118.100518 UR - https://global-sci.org/intro/article_detail/eajam/12942.html KW - Collocation method, SSP-RK(2, 2), telegraph equation, tri-diagonal solver, unconditional stability. AB -

A collocation method based on exponential B-splines for two-dimensional second-order non-linear hyperbolic equations is studied. The initial equation is split into a system of coupled equations, each of which is transformed into a system of ordinary differential equations. The corresponding differential equations are solved by SSP-RK(2,2) method. It is shown that the method under consideration is unconditionally stable. Numerical experiments demonstrate its efficiency and accuracy.

Swarn Singh, Suruchi Singh and Rajni Arora. (2019). An Unconditionally Stable Numerical Method for Two-Dimensional Hyperbolic Equations. East Asian Journal on Applied Mathematics. 9 (1). 195-211. doi:10.4208/eajam.280118.100518
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