Ahmad Fadly Nurullah Rasedee

2 point block backward difference method for solving Riccati type differential problems

A two point block backward difference method is established to solve Riccati differential equations directly. Based on a predictor-corrector two point block backward difference method (2PBBD), a code is developed using a set of integration coefficients that eliminates the need to be calculated at every step change. The method requires calculating the integration coefficients only once in the beginning. The 2PBBD has an added advantage of a recurrence relationship between coefficients of different orders which provides a more elegant algorithm. The recurrence relationship between coefficients also reduces the computational cost.

On equiconvergence of Fourier Series and Fourier Integral

In this paper we prove a precise equiconvergence relation between index of the Bochner-Riesz means of the expansions and power of the singularity of the distributions with compact support.

On the sufficient conditions of the localization of the Fourier-Laplace series of distributions from liouville classes

In this work we investigate the localization principle of the Fourier-Laplace series of the distribution. Here we prove the sufficient conditions of the localization of the Riesz means of the spectral expansions of the Laplace-Beltrami operator on the unit sphere.

Order and stability of 2-point block backward difference method

This paper studied the order and stability of a 2-Point Block Backward Difference method (2PBBD) for solving systems of nonstiff higher order Ordinary Differential Equations (ODEs) directly. The me...

The Wilkie model: A comparison of the discrete-time with the continuous-time

The Wilkie model is a stochastic asset model, developed by A.D Wilkie in 1984 with the purpose to explore the behavior of investment factors of insurer within the United Kingdom. The Wilkie model was considered as a discrete-time horizon model and we then reviewed the continuous time case which was initially introduced by Terence Chan in 1998. We comprehensively explain all four sub models in the Wilkie model and make comparison with the original Wilkie model in discrete time. Prior to that, we also discuss the famous Ornstein-Uhlenbeck process which will be used to develop the continuous-time Wilkie model.The Wilkie model is a stochastic asset model, developed by A.D Wilkie in 1984 with the purpose to explore the behavior of investment factors of insurer within the United Kingdom. The Wilkie model was considered as a discrete-time horizon model and we then reviewed the continuous time case which was initially introduced by Terence Chan in 1998. We comprehensively explain all four sub models in the Wilkie model and make comparison with the original Wilkie model in discrete time. Prior to that, we also discuss the famous Ornstein-Uhlenbeck process which will be used to develop the continuous-time Wilkie model.

Block variable order step size method for solving higher order orbital problems

Previous numerical methods for solving systems of higher order ordinary differential equations (ODEs) directly require calculating the integration coefficients at every step. This research provides a block multi step method for solving orbital problems with periodic solutions in the form of higher order ODEs directly. The advantage of the proposed method is, it requires calculating the integration coefficients only once at the beginning of the integration is presented. The derived formulae is then validated by running simulations with known higher order orbital equations. To provide further efficiency, a relationship between integration coefficients of various order is obtained.

Uniform convergence of the Fourier-Laplace series

This study examines the problem of uniform convergence for the functions from the Nikolskii class. The uniform convergences for the Riesz means of the Fourier-Laplace series in the Nikolskii class Hpa(SN) proved under certain conditions.

Absence of localization of Fourier-Laplace series

This article investigates a function f(x), constructed from the Nikol’skii class in S2. The estimation obtained will show that the Riesz mean of the spectral expansions is unable to be strengthened due to absence of localization caused by a singualrity at a definite point f(x), on the sphere.

Approximating of functions from Holder classes Hα[0, 1] by Haar wavelets

In the present work, a new direct computational method for solving definite integrals based on Haar wavelets is introduced. The definite integral of the functions from Holder classes is replaced with the approximation of the function by Haar wavelets and the the calculation of definite integrals is reduced to the problem of solving algebraic equation formed by the Fourier coefficients in terms of Haar wavelets. Based on the properties of the Haar wavelets it is shown that the such approximations much better approximate the value of the integrals for the functions from Holder classes. The Error analysis of the approximation method are worked out in the classes of Holder to show the efficiency of the new method and connection of the module of difference with smoothness of the function is established. Finally, some numerical examples of the implementation the method for the functions from Holder classes are presented.

On the Lebesgue constants of Fourier-Laplace series by Riesz Means

An asymptotic formula for the Lesbegue constant of the Riesz means of Fourier-Laplace series on the sphere obtained in this paper.