Mathematical and Computational Applications

1778 KiB

Open AccessArticle

A Perturbated Algorithm for Generalized Nonlinear Quasi-Variational Inclusions

by A.H. Siddiqi, Rais Ahmad and S. Husain

Math. Comput. Appl. 1998, 3(3), 177-184; https://doi.org/10.3390/mca3030177 - 01 Dec 1998

Viewed by 1067

In this paper, a perturbed iterative method for solving a generalized nonlinear quasi-variational inclusions, is presented and a convergence result which generalizes some known results in this field, is given. Full article

2331 KiB

Open AccessArticle

Pediatric Nutritional Requirements Determination with Neural Networks

by Bekir Karlık and Aydın Ece

Math. Comput. Appl. 1998, 3(3), 169-175; https://doi.org/10.3390/mca3030169 - 01 Dec 1998

Viewed by 1195

Abstract

To calculate daily nutritional requirements of children, a computer program has been developed based upon neural network. Three parameters, daily protein, energy and water requirements, were calculated through trained artificial neural networks using a database of 312 children The results were compared with [...] Read more.

To calculate daily nutritional requirements of children, a computer program has been developed based upon neural network. Three parameters, daily protein, energy and water requirements, were calculated through trained artificial neural networks using a database of 312 children The results were compared with those of calculated from dietary requirements tables of World Health Organisation. No significant difference was found between two calculations. In conclusion, a simple neural network may assist physicians in the determination of daily nutritional requirements. Full article

1456 KiB

Open AccessArticle

A Presentation Theorem of the Spherical Wave Functions

by Meryem Kaya

Math. Comput. Appl. 1998, 3(3), 161-167; https://doi.org/10.3390/mca3030161 - 01 Dec 1998

Viewed by 919

Abstract

Let \(\phi_{i}^{*}\) and \(\psi_{i} (i=0,1,...,n-1)\) are the solutions of the equations \(\boxdot^{2} - \frac{n-1}{r^{2}}\phi_{i}=0\) and \(\boxdot^{2} \psi_{i}=0\) respectively. In this paper it is shown that if \(u\) and \(v\) are satisfied by the equations \((\boxdot^{2} - \frac{n-1}{r^{2}})^{n} u = 0\) and \(\boxdot^{2n} v [...] Read more.

Let \(\phi_{i}^{*}\) and \(\psi_{i} (i=0,1,...,n-1)\) are the solutions of the equations \(\boxdot^{2} - \frac{n-1}{r^{2}}\phi_{i}=0\) and \(\boxdot^{2} \psi_{i}=0\) respectively. In this paper it is shown that if \(u\) and \(v\) are satisfied by the equations \((\boxdot^{2} - \frac{n-1}{r^{2}})^{n} u = 0\) and \(\boxdot^{2n} v =0\) respectively then \(u\) and \(v\) have the representations \(u=\phi_{0}^{*} + t\phi_{1}^{*} + ... + t^{n-1}\phi_{n-1}^{*}\) and \(v = \psi_{0} + t\psi+{1} + ... + t^{n-1}\psi_{n-1}\) where \(\boxdot^{2} = \frac{1}{r^{n-1}}\frac{\partial}{\partial r} (r^{n-1} \frac{\partial}{\partial r}) - \frac{\partial^{2}}{\partial r^{2}}\). Full article

2257 KiB

Open AccessArticle

A Comparison of Numerical ODE Solvers based on Euler Methods

by Mustafa İnç, Necdet Bildik and Hasan Bulut

Math. Comput. Appl. 1998, 3(3), 153-159; https://doi.org/10.3390/mca3030153 - 01 Dec 1998

Cited by 3 | Viewed by 1102

Abstract

A class of nonlinear methods based on Euler's integration formula for the numerical solution of ordinary differential equations is presented. Numerical example involving stiff linear systems of first-order differential equations are given for test problem. Full article

4228 KiB

Open AccessArticle

Boundary Emenet Formulation in Elastoplastic Stress Anaysis

by Halit Gun and A. Adib Becker

Math. Comput. Appl. 1998, 3(3), 139-151; https://doi.org/10.3390/mca3030139 - 01 Dec 1998

Viewed by 930

Abstract

This paper presents a review of different elasto-plastic Boundary Element (BE) formulations with particular emphasis on two main approaches; the initial strain displaccmcnt- gradient approach with its modeling of the partial or full interior domain, and the particular integral approach which can be [...] Read more.

This paper presents a review of different elasto-plastic Boundary Element (BE) formulations with particular emphasis on two main approaches; the initial strain displaccmcnt- gradient approach with its modeling of the partial or full interior domain, and the particular integral approach which can be applied exclusively to the surface avoiding any modeling interior. The initial strain formulation is implemcntcd in a computer program using two-dimensional isoparametric quatratic elements to discretise either the complete intcrior domain or only the part associated with the plastic region. The BE solutions are shown to bc in good agreement with analytical and Finite Elcment (FE) solutions. Full article

3209 KiB

Open AccessArticle

A Numerical Simulation of Melting of Ice Heated from above

by R. Kahraman, H. D. Zughbi and Y. N. Al-Nassar

Math. Comput. Appl. 1998, 3(3), 127-137; https://doi.org/10.3390/mca3030127 - 01 Dec 1998

Viewed by 1301

Abstract

Melting of ice in a cubical enclosure partially heated from above was studied. Half of the upper surface was maintained at room temperature and the other half at 70°C. The ice cube was maintained at its melting point at the bottom. The other [...] Read more.

Melting of ice in a cubical enclosure partially heated from above was studied. Half of the upper surface was maintained at room temperature and the other half at 70°C. The ice cube was maintained at its melting point at the bottom. The other side surfaces were insulated. The process was first modeled by ignoring the effect of natural convection in the liquid phase. The resulting equations of conservation of energy were solved in each phase. The motion of melting front was governed by an energy balance at the interface. This conduction model was verified by applying it to a I-D phase change problem for which an analytical solution is available. Preliminary experiments conducted resulted in a progress of the phase front faster than that predicted by the conduction model and the interface was smoother due to strong effects of natural convection in the liquid phase, except for the initial start of melting The model was then extended to include convective heat transfer in such a way that the liquid phase was assumed to be a mixed body subjected to natural convection from the top surface and the liquid-solid interface. The flux at the interface was obtained by finding a heat transfer coefficient for natural convection with a cold plate facing upward. The predictions of this convection model agreed well with the experimental results. Full article

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Math. Comput. Appl., Volume 3, Issue 3 (December 1998) – 6 articles , Pages 127-184

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