Journal of Progressive Research in Mathematics

On the computation of zeros of Bessel functions

Tahani E. Ahmed — 2023-01-12

The zeros of some chosen Bessel functions of different orders is revised using the well-known bisection method , McMahon formula is also reviewed and the calculation of some zeros are carried out implementing a recent version of MATLAB software.

The obtained results are analyzed and discussed on the lights of previous calculations.

Generalized Pierre Numbers

Yüksel Soykan — 2023-02-19

In this paper, we introduce and investigate the generalized Pierre sequences for the first time and we deal with, in detail, two special cases, namely, Pierre and Pierre-Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between Pierre, Pierre-Lucas and Tribonacci, Tribonacci-Lucas numbers.

Numerical Methods for Convex Quadratic Programming with Nonnegative Constraints

Qi Wang — 2023-03-05

This paper deals with some problems in numerical simulation for convex quadratic programming with nonnegative constraints. For systems of ordinary differential equations which derived from the above mentioned problem, we construct a kind of new numerical method: the modified implicit Euler method. Under some restrictions for step-size, we obtained the numerical solution which satisfied with the termination condition. Compared with the classical Matlab command ODE23, the new method has ideal computation cost.