Variable Step Block Hybrid Method for Stiff Chemical Kinetics Problems

A new variable step size block backward differentiation formula for solving stiff initial value problems

Local Annihilation Method ‎and‎ Some Stiff ‎Problems

In this article‎, ‎a new scheme inspired from collocation method is‎ ‎presented for numerical solution of stiff initial-value problems and Fredholm integral equations of the first kind based on the derivatives of residual function‎. ‎Then‎, ‎the error analysis‎ ‎of this method is investigated by presenting an error bound‎. ‎Numerical comparisons indicate that the‎ ‎presented method yields accur...

Variable Step Block Backward Differentiation Formula for Solving First Order Stiff ODEs

block method based on Backward Differentiation Formulae (BDF) of variable step size for solving first order stiff initial value problems (IVPs) for Ordinary Differential Equations (ODEs). In a 2-point Block Backward Differentiation Formula (BBDF), two solution values are produced simultaneously. Plots of their regions of absolute stability for the method are also presented. The efficiency of th...

Fifth Order Variable Step Block Backward Differentiation Formulae for Solving Stiff ODEs

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...

A Variable Step-Size Exponentially Fitted Explicit Hybrid Method for Solving Oscillatory Problems

An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1, x, exp μx , exp −μx }, μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of ...