Dissertation > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations

Non-polynomial Cubic Spline Methods for Solving One-Dimensional Parabolic Equations

Author YangTao
Tutor ZhaoPeiHao
School Lanzhou University
Course Basic mathematics
Keywords one dimensional parabolic equation non-polynomial cubic spline function difference scheme boundary value problems conditionally stable
CLC O241.82
Type Master's thesis
Year 2010
Downloads 27
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In this paper, based on the non-polynomial spline function, a family of difference schemes for solving one dimensional parabolic equation initial boundary value problems are constructed firstly. By choosing suitable parameters, many difference schemes may be derived from our methods, and we obtain a high accuracy three-level difference scheme, the accuracy of this scheme is fourth-order in time and space direction. Secondly, a new method is presented to deal with the Neumann boundary value problem, the accuracy of this method in space direction is improved to fourth-order. Finally, the numerical results show that our methods are very efficient.

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