Abstract A major challenge in simulating chemical reaction processes is integrating the stiff systems of Ordinary Differential Equations (ODEs) describing reactions due to stiffness. Thus, it would be interest search systematically for solvers that are close optimal such problems. This paper presents an implicit 3-Point Block Backward Differentiation Formula with one off-step point (3POBBDF) so...

We present a new stability analysis for the second barycentric formula, showing that this formula is backward stable when the relevant Lebesgue constant is small.

A variable step size multi-block backward differentiation formula for solving stiff initial value problems of ordinary differential equations with a strategy was derived. The proposed method (VSSMBBDF) computes two approximate solution values at time per integration step. stability properties are achieved by varying the ratio in to generate more zero stable schemes. is also found be an A-Stable...

The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. equations consist reaction-diffusion equation for the substrate concentration and fourth-order Cahn–Hilliard-type volume fraction biomass, considered in domain with no-flux boundary conditions. main difficulties are coming from degenerate diffusivity mobility, singular potential arising logar...

We consider fitting an ODE model to time series data of the system variables. We assume that the parameters of the model have some initial range of possible values and the goal is to reduce these ranges to produce a smaller parameter region from which to start a global nonlinear optimization algorithm. We introduce the class of cumulative backward differentiation formulas (CBDFs) and show that ...

Singular source terms in sub-diffusion equations may lead to the unboundedness of solutions, which will bring a severe reduction convergence order existing time-stepping schemes. In this work, we propose two efficient schemes for solving with class mildly singular time. One discretization is based on Grünwald-Letnikov and backward Euler methods. First-order error estimate respect time rigorousl...

The implicit block methods based on the backward differentiation formulae (BDF) for the solution of stiff initial value problems (IVPs) using variable step size is derived. We construct a variable step size block methods which will store all the coefficients of the method with a simplified strategy in controlling the step size with the intention of optimizing the performance in terms of precisi...

The following experiment examined the effect of noncontact therapeutic touch (NCTT) on the regeneration rate of salamander forelimbs surgically amputated through the distal third of the stylopodium. A total of 154 newts, Notophthalmus viridescens, were used and limb regeneration was assessed using two criteria: (1) the time to first finger differentiation, and (2) the time to fourth finger diff...

A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a hi...