An efficient method for the numerical evaluation of partial derivatives of arbitrary order
ACM Transactions on Mathematical Software (TOMS)
Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
SIAM Journal on Scientific Computing
Radial basis collocation methods for elliptic boundary value problems
Computers & Mathematics with Applications
International Journal of Computer Mathematics
Hi-index | 0.09 |
In this paper, a numerical method for solving the linear initial problems for partial differential equations with constant coefficients and analytic initial conditions in two and three independent variables is presented. The technique is based upon the Taylor series expansion. Properties and the operational matrices for partial derivatives for the Taylor series in two and three variables are first presented. These properties are then used to reduce the solution of partial differential equations in two and three independent variables to a system of algebraic equations. The procedure can be extended to linear partial differential equations with more independent variables. The Taylor series may not converge if the solution is not analytic in the whole domain, however, the present method can be applied to boundary-value problems for linear partial differential equations, when the solution is analytic in the interior of the domain and also on some open subsets for each distinct part of the boundary. The method is computationally very attractive and applications are demonstrated through illustrative examples.