Block backward differentiation formulas for solving fuzzy differential equations under generalized differentiability

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

Derivation of BBDF-α for solving ordinary differential equation

In this paper, the block backward differentiation formulas with parameter α (BBDF-α) of order three is derived in a constant step size for solving system of first order ordinary differential equations (ODEs). The coefficients of formula are generated using Maple software package. The influence of parameter α is considered to produce better approximate solutions at two points simultaneously. Numerical experiment is included to show the capability of the derived method in solving ODEs. Numerical results indicate that the BBDF-α outperforms the existing methods in term of accuracy

Convergence properties of pth order diagonally implicit block backward differentiation formulas

This paper investigates the convergence properties for diagonally implicit 2-point block backward differentiation formulas of order two, three and four. The formulation of the method is reviewed from the literature. The order of the method is verified. The concepts of consistency and zero stability are considered to prove the convergence of the method

Diagonally implicit block backward differentiation formulas for solving fuzzy differential equations

In this work, the diagonally implicit 2-points block backward differentiation formulas (DIBBDF) is developed for solving Fuzzy Differential Equations (FDEs) under the interpretation of generalized Hukuhara differentiability. The fuzzy configuration of this method is also introduced. Numerical results using DIBBDF are presented and compared with the existing method. It is clearly shown that the proposed method obtains good numerical results and suitable for solving FDEs

On the stability of diagonally implicit 2-point block backward differentiation formulae

In this work, the zero-stability properties of diagonally implicit 2-point block backward differentiation formulas (DI2BBDF) are presented. The stability region is illustrated to prove the A-stable behavior. Some numerical stiff problems are provided to test the performance of the method in terms of accuracy. Numerical results are compared with the fully implicit 2-point block backward differentiation formulas (FI2BBDF)

Variable order block method for solving second order ordinary differential equations

This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are produced simultaneously at each step. All the three different orders of 2-point BBDF is implemented in variable order scheme. The scheme utilizes the local truncation error, which is generated by the single order of 2-point BBDF method. Numerical results are presented to illustrate the validity of the proposed scheme

Variable order block method for solving second order ordinary differential equations

This paper proposed 2-point block backward differentiation formulas (BBDF) of order 3, 4, and 5 for direct solution of second order ordinary differential equations. These methods were derived via backward difference interpolation polynomial with two solutions are produced simultaneously at each step. All the three different orders of 2-point BBDF is implemented in variable order scheme. The scheme utilizes the local truncation error, which is generated by the single order of 2-point BBDF method. Numerical results are presented to illustrate the validity of the proposed scheme

A Framework For Chili Fruits Maturity Estimation Using Deep Convolutional Neural Network

An agriculture robot has been demanded in recent years. Inaccurate in estimating the maturity of the chili always happens since the human eyes are tend to prone to errors. Serving an effective, innovative, feasible chili recognition system would help farmers as economical alternative by reducing the workloads while increasing fruit yield. Hence, a comprehensive framework of chili maturity estimation using deep learning is carried out