{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T16:52:53Z","timestamp":1761929573454},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> In this paper, we propose a new high accuracy discretization based on the ideas given by Chawla and Shivakumar for the solution of two-space dimensional nonlinear hyperbolic partial differential equation of the form u<jats:sub>tt<\/jats:sub> = A(x, y, t)u<jats:sub>xx<\/jats:sub> + B(x, y, t)u<jats:sub>yy<\/jats:sub> + g(x, y, t, u, u<jats:sub>x<\/jats:sub>, u<jats:sub>y<\/jats:sub>, u<jats:sub>t<\/jats:sub>), 0 &lt; x, y &lt; 1, t &gt; 0 subject to appropriate initial and Dirichlet boundary conditions. We use only five evaluations of the function g and do not require any fictitious points to discretize the differential equation. The proposed method is directly applicable to wave equation in polar coordinates and when applied to a linear telegraphic hyperbolic equation is shown to be unconditionally stable. Numerical results are provided to illustrate the usefulness of the proposed method. <\/jats:p>","DOI":"10.1142\/s179396231150005x","type":"journal-article","created":{"date-parts":[[2011,12,30]],"date-time":"2011-12-30T10:46:59Z","timestamp":1325242019000},"page":"1150005","source":"Crossref","is-referenced-by-count":6,"title":["HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS"],"prefix":"10.1142","volume":"03","author":[{"given":"R. K.","family":"MOHANTY","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi-110 007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VENU","family":"GOPAL","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Delhi, Delhi-110 007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,10]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1975-0416049-2"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1978-0483507-7"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015160900410"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(95)00201-4"},{"key":"rf5","first-page":"983","volume":"22","author":"Mohanty R. K.","journal-title":"Numer. Meth. Part Differ. Equat."},{"key":"rf6","first-page":"799","volume":"152","author":"Mohanty R. 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