In this paper, the fully implicit 2-point block backward differentiation formula and diagonally implicit 2-point block
backward differentiation formula were developed under the interpretation of generalized differentiability concept for
solving first order fuzzy differential equations. Some fuzzy initial value problems were tested in order to demonstrate the
performance of the developed methods. The approximated solutions for both methods were in good agreement with the
exact solutions. The numerical results showed that the diagonally implicit method outperforms the fully implicit method
in term of accuracy.
In this paper, we study the numerical method for solving second order Fuzzy
Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF)
under generalized concept of higher-order fuzzy differentiability. Implementation of
the method using Newton iteration is discussed. Numerical results obtained by BBDF
are presented and compared with Backward Differential Formulas (BDF) and exact
solutions. Several numerical examples are provided to illustrate our methods.
In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting method. Most of the existence researches involved BVPs will reduce the problem to a system of first order ODEs. This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this paper will be utilised to obtain a series solution of the initial value problems directly without reducing to first order equations. The numerical results show that the proposed method with shooting method can produce good results.
This paper describes the development of a two-point implicit code in the form of fifth order Block Backward Differentiation Formulas (BBDF(5)) for solving first order stiff Ordinary Differential Equations (ODEs). This method computes the approximate solutions at two points simultaneously within an equidistant block. Numerical results are presented to compare the efficiency of the developed BBDF(5) to the classical one-point Backward Differentiation Formulas (BDF). The results indicated that the BBDF(5) outperformed the BDF in terms of total number of steps, accuracy and computational time.