1.2CAMar 9, 2018
On Computing Jacobi's Elliptic Function \texttt{sn}Ernest Scheiber
The paper presents a method to compute the Jacobi's elliptic function \texttt{sn} on the period parallelogram. For fixed $m$ it requires first to compute the complete elliptic integrals $K=K(m)$ and $K'=K(1-m).$ The Newton method is used to compute sn(z,m), when $z\in [0,K]\cup[0,i K').$ The computation in any other point does not require the usage of any numerical procedure, it is done only with the help of the properties of sn.
1.2NAAug 8, 2017
On the numerical Picard iterations method with collocations for the IVPErnest Scheiber
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand side of the differential system by Lagrange interpolation polynomials followed by successive approximations. In the case when the number of interpolation point is fixed a convergence result is given. Finally some numerical experiments are reported.
1.2NASep 6, 2015
On the Convergence of the Variational Iteration MethodErnest Scheiber
Convergence results are stated for the variational iteration method applied to solve an initial value problem for a system of ordinary differential equations.
1.2NAApr 18, 2015
On the Chebyshev approximation of a function with two variablesErnest Scheiber
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is given an uniform convergence result.