Continuous block backward differentiation formula for solving stiff ordinary differential equations

Application of the block backward differential formula for numerical solution of Volterra integro-differential equations

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations

This paper focuses on the derivation of diagonally implicit two-point block backward differentiation formulas DI2BBDF for solving first-order initial value problem IVP with two fixed points. The method approximates the solution at two points simultaneously. The implementation and the stability of the proposed method are also discussed. A performance of the DI2BBDF is compared with the existing ...

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

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...

A quasi-interpolation method for solving stiff ordinary differential equations