Abstract: A class of meshless methods for heat conduction equations are constructed.They can be performed on structured or unstructured meshes.The methods are conservative and consistent.They have at least the first order accuracy when performed on irregular quadrilateral or triangular meshes,and have the second order accuracy when performed on rectangular or uniform parallelogram meshes. These meshless methods are suitable and efficient in solving linear or nonlinear parabolic problems on irregular quadrilateral meshes or mixed meshes, especially in solving two-dimensional three-temperature radiation heat conduction equations on irregular and mixed meshes.

Key words: heat conduction equations, meshless methods, radiation hydrodynamics, irregular meshes