Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations

•We propose a fast error estimation method for LRBF for the first time.•Based on the error estimation method, we propose an adaptive shape parameter selection strategy for LRBF for the first time, and give a complete process.•A particle swarm optimization algorithm is used to realize the complete process proposed above, and the feasibility of this method is verified by using test functions and multi type boundary problems.