A Modified WPE Method For Solving Fokker-Planck Equations In Molecular Motors Models

In mathematical models,the motion of an ensemble of molecular motors is described by Fokker-Planck equations,but traditional numerical algorithms cannot effectively solve discontinuous cases.The WPE method still works when the potential is discontinuous.Unfortunately,the accuracy of the WPE method will drop to first order.The improved WPE method maintains the second order accuracy even when the potential is discontinuous.However,it is a different approach for calculating the jump rates and does not point out the reason why accuracy will drop.Here a modified version of the WPE method is proposed.The modified WPE method still makes use of local solutions to obtain the jump rates and find the reason why accuracy will drop.The modified WPE method maintains the second order accuracy even when the potential is discontinuous and satisfies the necessary condition for the convergence of the numerical method at the discontinuity.