{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:11:45Z","timestamp":1762431105397},"reference-count":32,"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":[[2016,6]]},"abstract":"<jats:p> We demonstrate a new nonuniform mesh finite difference method to obtain accurate solutions for the elliptic partial differential equations in two dimensions with nonlinear first-order partial derivative terms. The method will be based on a geometric grid network area and included among the most stable differencing scheme in which the nine-point spatial finite differences are implemented, thus arriving at a compact formulation. In general, a third order of accuracy has been achieved and a fourth-order truncation error in the solution values will follow as a particular case. The efficiency of using geometric mesh ratio parameter has been shown with the help of illustrations. The convergence of the scheme has been established using the matrix analysis, and irreducibility is proved with the help of strongly connected characteristics of the iteration matrix. The difference scheme has been applied to test convection diffusion equation, steady state Burger\u2019s equation, ocean model and a semi-linear elliptic equation. The computational results confirm the theoretical order and accuracy of the method. <\/jats:p>","DOI":"10.1142\/s1793962316500069","type":"journal-article","created":{"date-parts":[[2015,12,23]],"date-time":"2015-12-23T07:15:29Z","timestamp":1450854929000},"page":"1650006","source":"Crossref","is-referenced-by-count":6,"title":["An exponential expanding meshes sequence and finite difference method adopted for two-dimensional elliptic equations"],"prefix":"10.1142","volume":"07","author":[{"given":"Navnit","family":"Jha","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neelesh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Department of Mathematics, South Asian University, Chanakyapuri, New Delhi 110 021, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,6,2]]},"reference":[{"key":"S1793962316500069BIB001","volume-title":"Handbook of Linear Partial Differential Equations for Engineers and Scientists","author":"Polyanin A. 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