A NEW SUPERCLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR 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...

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

application of the block backward differential formula for numerical solution of volterra integro-differential equations

in this paper, we consider an implicit block backwarddifferentiation formula (bbdf) for solving volterraintegro-differential equations (vides). the approach given in thispaper leads to numerical methods for solving vides which avoid theneed for special starting procedures. convergence order and linearstability properties of the methods are analyzed. also, methods withextensive stability region ...

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 ...

Fully Implicit 3-Point Block Extended Backward Differentiation Formula for Stiff Initial Value Problems

A new block extended backward differentiation formula suitable for the integration of stiff initial value problems is derived. The procedure used involves the use of an extra future point which helps in improving the performance of an existing block backward differentiation formula. The method approximates the solution at 3 points simultaneously at each step. Accuracy and stability properties o...