The computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

The High-Dimensional Model Representation (HDMR) technique is a family of approaches to efficiently interpolate high-dimensional functions. RS(Random Sampling)-HDMR is a practical form of HDMR based on randomly sampling the overall function, and utilizing orthonormal polynomial expansions to approximate the RS-HDMR component functions. The determination of the expansion coefficients for the com...

One of the main purposes of spatio-temporal modeling is to replay and reproduce states at different historical moments. The spatio-temporal data integration is the key to building the model because it exerts a direct influence on the mode and efficiency of querying data in the database. In fact, in the previous study, the author has proposed a time-based spatiotemporal data integration method a...

Reaction networks in the bulk and on surfaces are widespread in physical, chemical, and biological systems. In macroscopic systems, which include large populations of reactive species, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations. However, many physical systems are partitioned into microscopic domains, where the number of molecules in each ...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

Phase retrieval from unidirectional radiographic differential phase contrast images requires integration of noisy data. A method is presented, which aims to suppress stripe artifacts arising from direct image integration. It is purely algorithmic and therefore, compared to alternative approaches, neither additional alignment nor an increased scan time is required. We report on the theory of thi...