A Closer Look at the Heat Equation

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Márkus Oszkar (Editor)

Series: Mathematics Research Developments
BISAC: MAT007020

This compilation begins by presenting high order accurate numerical methods for solving the heat equation on general smooth regions in two dimensions. The methods use fourth order accurate techniques that the authors have developed for evaluating certain volume and surface integrals over the regions on which the differential equation is defined.

In addition, the authors propose some parallel programs for solving the heat equation which have been discretized using the finite difference method. These programs have been implemented through different parallel languages such as SkelGIS library, Compute Unified Device Architecture and Streams and Iterations in Single Assignment Language.

The n-dimensional heat equation is studied through the Diamond Bessel operator. The solution is found by the methods of convolution and Fourier transform in distribution theory, and the Bessel heat kernel is acquired.

The closing study solves the nonlinear diamond heat equation, obtaining the solution in the compact subset of Rn _(0;1), as well as obtaining an interesting diamond heat kernel related to the nonlinear heat equation.

(Imprint: Novinka)

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Table of Contents

Preface

Chapter 1. High Order Accurate Numerical Solution of the Heat Equation
(Anita Mayo, Baruch College, New York, NY, US)

Chapter 2. Implementation of Parallel Algorithm for Heat Equation Using CUDA, SkelGIS Library and SISAL
(S. Belhaous, S. Chokri, S. Baroud, Z. Hidila and M. Mestari, Department of Mathematics and Computer science, Hassan II University, Mohammedia, Morocco)

Chapter 3. On the Bessel Heat Equation in N-Dimensional Related to Diamond Bessel Operator
(Wanchak Satsanit, Department of Mathematics, Faculty of Science, Maejo University, Chiangmai, Thailand)

Chapter 4. On the Mixed Operator for Solving Nonlinear Diamond Heat Equation
(Wanchak Satsanit, Department of Mathematics, Faculty of Science, Maejo University, Chiangmai, Thailand)

Index

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