The radial basis function method for 3D advection diffusion reaction equations with variable coefficients is presented. The proposed method implements the linear combination of radial basis functions which impose boundary conditions in advance, and thus such a combination with weighted parameters can be used to construct the final approximation. Furthermore, the weighted parameters are solved by substituting the approximation into governing equations. This method leads to crucial improvements in the feasibility and accuracy which can now be easily applied to general 3D nonlinear problems through linearized techniques. Finally, accuracy and efficiency of the proposed method are verified by several examples.

中文翻译：

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变系数3D线性和非线性对流扩散反应方程的一种新的径向基函数方法

提出了具有可变系数的3D对流扩散反应方程的径向基函数方法。所提出的方法实现了预先施加边界条件的径向基函数的线性组合，因此这种与加权参数的组合可用于构建最终近似。此外，通过将近似代入控制方程来求解加权参数。这种方法极大地提高了可行性和准确性，现在可以通过线性化技术轻松地将其应用于一般 3D 非线性问题。最后，通过几个算例验证了所提方法的准确性和有效性。