Mohanty, R. K.; Evans, D. J.; Kumar, Dinesh High accuracy difference formulae for a fourth order quasi-linear parabolic initial boundary value problem of first kind. (English) Zbl 1026.65069 Int. J. Comput. Math. 80, No. 3, 381-398 (2003). Summary: New three level implicit finite difference methods of \(O(k^2+ h^2)\) and \(O(k^3+ h^4)\) are proposed for the numerical solution of fourth-order quasi-linear parabolic partial differential equations in one space variable, where \(k> 0\) and \(h> 0\) are grid sizes in time and space coordinates respectively. In both cases, we use only nine grid points. The numerical solution of \(\partial u/\partial x\) is obtained as a by-product of the method. The characteristic equation for a model problem is established. Application to a linear singular equation is also discussed in detail. Four examples illustrate the utility of the new difference methods. Cited in 5 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 35K55 Nonlinear parabolic equations Keywords:error bounds; numerical examples; fourth-order quasi-linear parabolic equation; singular equation; RMS errors; implicit finite difference methods PDFBibTeX XMLCite \textit{R. K. Mohanty} et al., Int. J. Comput. Math. 80, No. 3, 381--398 (2003; Zbl 1026.65069) Full Text: DOI References: [1] Crandall S. H., J. Assoc. Comp. Mach. 1 pp 111– (1954) [2] Conte S. D., J. Assoc. Comp. Mach. 4 pp 18– (1957) [3] DOI: 10.1093/comjnl/8.3.280 · Zbl 0134.33006 · doi:10.1093/comjnl/8.3.280 [4] DOI: 10.1090/S0025-5718-1967-0221785-2 · doi:10.1090/S0025-5718-1967-0221785-2 [5] DOI: 10.1002/nme.1620100614 · Zbl 0345.65047 · doi:10.1002/nme.1620100614 [6] DOI: 10.1016/0045-7825(83)90054-3 · Zbl 0509.65044 · doi:10.1016/0045-7825(83)90054-3 [7] DOI: 10.1080/00207169108804004 · Zbl 0736.65061 · doi:10.1080/00207169108804004 [8] DOI: 10.1016/S0377-0427(99)00202-2 · Zbl 0963.65083 · doi:10.1016/S0377-0427(99)00202-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.