Search results

This paper deals with the use of the combined Adomian/Alienor methods for solving the problem of optimal cancer chemotherapy model.

The combination of the Adomian decomposition method and the Alienor reducing transformation method allows us to solve the control problem as if it were a classical one dimensional minimization problem. The mathematical model used here describes specific model based on cell‐cycle kinetics.

It was found that the goal is to maintain the number of the cancerous cells around a desired value while keeping the toxicity to the normal tissues acceptable.

Simulation results are given for illustration.

New combined approach to optimal control of cancer chemotherapy using Adomian/Alienor Methods.

The purpose of this paper is to show that a combination of Adomian and Alienor methods can be used to solve the problem of parameters identification of HIV/AIDS model. This model involves a system of three ordinary differential equations.

Parameters identification leads to the minimization of an error functional given by the sum of variations between measured variables and calculated variables obtained by solving the system of differential equations. We assume that the quantity of healthy cells CD4 + T and the viral load contents in the blood are measured.

The identification was realized by applying the combined Adomian/Alienor method allowing to reduce the problem to a minimization problem in dimention one.

Simulation results are given for illustration.

Application to parameter identification in an HIV model‐compatible, results to other methods.

Aims to propose methodology to solve adaptive control problems by the use of the Adomian decomposition method (ADM).

The approach to this problem is through the ADM which consists in finding a solution of nonlinear state equations as a convergent series that depends on the unknown parameters of the system.

It was shown that a first approach for solving adaptive control problems could be tackled by using the ADM. The solution of the systems was obtained in a series forms as a function of the unknown parameters. The objective function became a function that explicitly depends on parameters. This, it was shown, can be minimised by classical or nonclassical global optimization methods.

The methods presented depends on ADM. It is proposed that future work involves the study of an adaptive control problem associated to a nonlinear compartmental systems of Michaels‐Menten type.

Presents an applications of the developed ADM using it, as adapted to control problems. It contributes to mathematical modelling studied concerning most biological, physical phenomena which are described by nonlinear systems: differential, partial differential in form and for which there is little hope of finding an exact solution.

This paper aims at applying the proven Adomian and Alienor methods to solve the problem of optimal chemotherapy of HIV model.

The combination of the Adomian decomposition method and the Alienor reduction method allows us to solve the control problem as if it were a classical one‐dimensional minimization problem. The methodology is applied to a HIV model and simulation results given.

A general abstract framework for the control of a non‐linear evolution system has been developed. It was shown that it is possible to control a system by using the powerful techniques of Adomian and Alienor, and produce results comparable with those obtained by classical methods where other cost functions are used.

The benefit of this work is based on the CD4 healthy cells being maximized and the cost based on a drug dose being minimized. The new methodology could be used after further research for solving many control problems in biology and in other areas such as those involving industrial processes.

New methodology is cost‐effective in controlling the drug dose affecting rate of infection of cells by HIV virus.

New application of proven methodology will solve many control problems in biocybernetics/biomedicine/industry and other fields.

In this paper, non‐linear compartment modelling is used to study drug transport of anticancerous substance across brain tissues. The aim of the work is to identify the pharmacokinetic parameters of the model created.

A combination of the Adomian decomposition method and the Alienor reducing transformation method were used to solve the identification problem as if it were a classical one‐dimensional minimization problem.

The numerical results using this methodology have shown that local therapeutic method should be preferred, when it comes to evaluate the rate (of healthy cells/cancerous cells), especially when, somehow, the drug transition into the tumour is speeded up. The combination method of Adomian and Alienor proved a successful strategy, and could take into account many of the pharmacokinetic parameters as necessary and use well‐known algorithms.

It is believed that this modest work can be considered as preliminary steps for improving local drug administration.

The study has shown that pharmacokinetic/pharmacodynamic modelling can help to understand the drug behaviour in such complex media and hence avoid the most threatening side effects by predicting the toxicity threshold of a drug and therefore minimize the therapeutic index.

Shows the powerful tools of Adomian and Alienor techniques that can be applied successfully in biomedical applications.

The purpose of this paper is to propose a new modification of the Adomian decomposition method for resolution of higher‐order inhomogeneous nonlinear initial value problems.

First the authors review the standard Adomian decomposition scheme and the Adomian polynomials for solving nonlinear differential equations. Next, the advantages of Duan's new algorithms and subroutines for fast generation of the Adomian polynomials to high orders are discussed. Then algorithms are considered for the solution of a sequence of first‐, second‐, third‐ and fourth‐order inhomogeneous nonlinear initial value problems with constant system coefficients by the new modified recursion scheme in order to derive a systematic algorithm for the general case of higher‐order inhomogeneous nonlinear initial value problems.

The authors investigate seven expository examples of inhomogeneous nonlinear initial value problems: the exact solution was known in advance, in order to demonstrate the rapid convergence of the new approach, including first‐ through sixth‐order derivatives and quadratic, cubic, quartic and exponential nonlinear terms in the solution and a sextic nonlinearity in the first‐order derivative. The key difference between the various modified recursion schemes is the choice of the initial solution component, using different choices to partition and delay the subsequent parts through the recursion steps. The authors' new approach extends this concept.

The new modified decomposition method provides a significant advantage for computing the solution's Taylor expansion series, both systematically and rapidly, as demonstrated in the various expository examples.

The paper's purpose is to promote the use of modern technologies such as multimedia packages to engineering students. The aim is to help them to learning in their learning, visualization, problem solving and understanding engineering concepts such as in mechanics dynamics.

TAPS packages are developed to help students solve selected engineering problems in a step‐by‐step approach. A comparison is made with existing commercial engineering packages to see if TAPS packages could further enhance the learning process.

The differences found were indicative of better presentation and clarity, step‐by‐step approach to solve engineering problems, user‐friendly environment, unbiased assessment of performance and flexibility to incorporate 3‐D geometric models in the TAPS packages.

The TAPS packages were compared with two commercial engineering packages and were based on a small number of users. A larger sample size of students would be required to see if TAPS packages are productive enough to be used locally in Malaysian universities and higher learning institutions.

The main originality of the paper can be seen from the development of the TAPS packages and the comparative study with existing commercial engineering packages. The differences found are explained in details in this paper.

This paper aims to develop a new real‐time effective method for solving the inverse kinematics (IK) problem, especially for those manipulators with high‐dimensional nonlinear kinematic equations.

The paper transforms the IKs problem into a minimization problem. Then, a novel meta‐heuristic algorithm, called the electromagnetism‐like method (EM), is used to solve this equivalent problem. Moreover, in order to further improve the computational efficiency and accuracy of EM, a hybrid method which combines EM with the Davidon‐Fletcher‐Powell (DFP) method is proposed.

The results showed that EM is a powerful yet easy algorithm for solving the IKs problem of robot manipulators. Its complexity is independent on the characteristics of the kinematic equations involving dimensionality and the degree of nonlinearity. Moreover, EM can be used as an accompanying algorithm for DFP method to get better precision at a lower iteration number.

The method developed in this paper is a generalized approach that is efficient enough to obtain IK solutions independent of robot geometry and the number of degrees of freedom.

This paper aims to present the development of technology‐assisted problem solving (TAPS) packages at University Tenaga Nasional (UNITEN). The project is the further work of the development of interactive multimedia based packages targeted for students having problems in understanding the subject of engineering mechanics dynamics.

In this study TAPS packages are compared with other selected engineering computer packages.

The differences found were indicative of better presentation and clarity, step‐by‐step approach to solve engineering problems, user‐friendly environment, unbiased assessment of performance and flexibility to incorporate 3‐D geometric models in the TAPS packages.

This paper provides a brief account of the differences between the TAPS packages approach used in this research with that of commercial simulation packages accompanying the engineering mechanics dynamics textbook and will be of interest to those in the field of engineering.