Determination of one dimensional temperature distribution in metallic bar using green's function method

Virginia Mwelu Kitetu; Thomas Onyango; Jackson Kioko Kwanza; Nicholas Muthama Mutua

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Determination of one dimensional temperature distribution in metallic bar using green's function method

机译：用格林函数法确定金属棒中的一维温度分布

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The present study focuses on determination of temperature distribution in one dimensional bar using Green's function method. The Green's Function is obtained using separation of variables, variation formulation principles and Heaviside functions. The Boundary Integral Equation is obtained using the fundamental solution, Divergence theorem, Green Identities, Dirac delta properties and integration by parts. The solution of heat equation given by the Green's Function and the boundary integral equation has satisfied the uniqueness, regularity and stability of heat equation. The uniqueness, regularity and stability have been proved using smooth properties of class k function, Lyapunov function and L~2 Norm. The BEM implementation is performed using FORTRAN 95 software. Solutions to the test problems are presented and time dependence results are in agreement with computed analytical solutions.

机译：本研究着重于使用格林函数法确定一维条形中的温度分布。格林函数是通过变量分离，变量表述原理和Heaviside函数获得的。边界积分方程是使用基本解，散度定理，绿色恒等式，狄拉克增量性质和零件积分获得的。由格林函数和边界积分方程给出的热方程的解满足了热方程的唯一性，规律性和稳定性。利用k类函数，Lyapunov函数和L〜2范数的光滑性质证明了其唯一性，规则性和稳定性。 BEM实施是使用FORTRAN 95软件执行的。提出了测试问题的解决方案，并且时间依赖性结果与计算的分析解决方案一致。

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《American Journal of Applied Mathematics》 |2013年第4期|共16页
作者
Virginia Mwelu Kitetu; Thomas Onyango; Jackson Kioko Kwanza; Nicholas Muthama Mutua;
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Determination of one dimensional temperature distribution in metallic bar using green's function method

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