Use Improved Gradient Descent in Irregular Boundary Conditions in Molecular Dynamics

An improvement is made on the adaptive step size of the gradient Descent (GD). We propose that the improved GD can be used in Molecular Dynamics (MD) to determine the shortest distance between an irregular curve (described in high-order equation) and a point outside the curve, that we show that it can solve the problem with affordable computational power and high accuracy (an average of 1% error in around 30 iterations).

On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.