1 Introduction Chain-of-Thought(CoT)prompting[1]has enhanced the performance of Large Language Models(LLMs)across various reasoning tasks.However,CoT still falls short in dealing with complex math word problems.As sho...1 Introduction Chain-of-Thought(CoT)prompting[1]has enhanced the performance of Large Language Models(LLMs)across various reasoning tasks.However,CoT still falls short in dealing with complex math word problems.As shown in Fig.1,CoT usually suffers from three pitfalls:semantic misunderstanding errors,calculation errors,and step-missing errors.Prior studies[2]involve addressing the calculation errors and step-missing errors,but neglect the semantic misunderstanding errors,which is the major factor limiting the reasoning performance of LLMs.展开更多
An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the...An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.623B2076,U23B2048 and 62225113)in part by the Science and Technology Major Project of Hubei Province(2024BAB046)in part by the Science and Technology Project of State Grid Corporation of China(5700-202458333A-2-1-ZX).
文摘1 Introduction Chain-of-Thought(CoT)prompting[1]has enhanced the performance of Large Language Models(LLMs)across various reasoning tasks.However,CoT still falls short in dealing with complex math word problems.As shown in Fig.1,CoT usually suffers from three pitfalls:semantic misunderstanding errors,calculation errors,and step-missing errors.Prior studies[2]involve addressing the calculation errors and step-missing errors,but neglect the semantic misunderstanding errors,which is the major factor limiting the reasoning performance of LLMs.
文摘An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.
