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首页> 外文期刊>Journal of Computational and Applied Mathematics >Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates
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Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates

机译：在球坐标系中具有Neumann边界条件的N载体系统中求解3D微观传热模型的精确有限差分方案

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摘要

In this study, we propose a 3D generalized micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates, which can be applied to describe the non-equilibrium heating in biological cells. Two improved unconditionally stable Crank-Nicholson schemes are then presented for solving the generalized model. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Neumann boundary condition can be applied directly without discretization. As such, a second-order accurate finite difference scheme without using any fictitious grid points is obtained. The convergence rates of the numerical solution are tested by an example. Results show that the convergence rates of the present schemes are about 2.0 with respect to the spatial variable r, which improves the accuracy of the Crank-Nicholson scheme coupled with the conventional first-order approximation for the Neumann boundary condition.
机译：在这项研究中，我们提出了一种在球面坐标系中具有Neumann边界条件的N载体系统中的3D广义微热传递模型，该模型可用于描述生物细胞中的非平衡加热。然后提出了两种改进的无条件稳定的Crank-Nicholson方案来求解广义模型。尤其是，我们会微调调整边界附近的内部网格点的位置，以便可以直接应用Neumann边界条件而无需离散化。这样，获得了不使用任何虚拟网格点的二阶精确有限差分方案。通过一个例子测试了数值解的收敛速度。结果表明，相对于空间变量r，本方案的收敛速度约为2.0，这提高了Crank-Nicholson方案的精度，并结合了针对Neumann边界条件的常规一阶逼近。

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