In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm---Volterra integrodifferential equations. The solution meth...

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical systems is to use fuzzy differential equations. In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability. The analytic and approximate solutions are given with series form in terms of their parametric form in the space $$W_2^2 [a,b]\oplus W_2^2 [a,b].$$W22[a,b]źW22[a,b]. The method used in this paper has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, needs less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions and their derivatives will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this paper show potentiality, generality, and superiority of our method as compared with other well-known methods.

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation in the space $$\oplus _{j=1}^2 W_2^3 \left[ {a,b}\right] $$źj=12W23a,b. An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.

Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates

The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.

Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions

A numerical method for singularly perturbed turning point problems with an interior layer

Huffman coding is an optimal coding method in information theory, but it requires statistical properties of coded data, and can not be realized by hardware in real-time. In this paper, a new data coding method, base-bit+overflowing-bit, is proposed. This coding method does not require statistical properties of coded data and can be realized in real- time. Experiments show that 2 - 3 times compression ratio can be obtained after coding source data with this coding method. The implementation with hardware is also described in the paper.

Real-time data compression implementation based on the base-bit + overflowing-bit coding

This paper describes a computer-aided performance evaluation system for testing and checking the on-board data compression system used in the High-Resolution Imaging Spectrometer (HIRIS). The earth resources spectra from the NASA earth resources spectral information system are taken for simulative spectra of ground objects, and these spectra are sampled and quantized according to the conditions and parameters of HIRIS. Then the simulative spectral data are put in a GIFOV spectral data generator through a computer interface. In testing, the spectral data stored in the generator are sent to the data compression system at the same rate of the readout clock of subdetectors in HIRIS. The data compression system compresses the input data in real-time under the control of the clock of the input data. After compressing, the compression results are returned to the computer through a bidirection interface and compared with the original ones. Finally, the computer gives out testing results. This kind of test system can exactly simulate the original data obtained by HIRIS in space, and objectively evaluate the data compression system.

Shuqiu Li

Papers

A numerical method for singularly perturbed turning point problems with an interior layer

Real-time data compression implementation based on the base-bit + overflowing-bit coding

Computer-aided performance evaluation system for the on-board data compression system in HIRIS