seminar

This talk focuses on an original framework for the stability and convergence analysis of implicit and implicit-explicit variable-step BDF3 schemes for linear and nonlinear parabolic equations. Under the new improved ratio restriction, robust stability and optimal error estimates utilizing a concise energy method in an abstract setting are obtained. The proposed framework is applicable to a wide range of nonlinear parabolic equations and demonstrates a promising approach for higher-order linear multi-step methods with variable step-sizes.