Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some numerical examples. تفاصيل المقالة

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the proposed method. تفاصيل المقالة

In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provides more accurate and numerically stable solutions. تفاصيل المقالة

In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. Weak form formulation of the discretized equations has been constructed on local subdomains, hence the domain and boundary integrals in the weak form methods can easily be evaluated over the regularly shaped subdomains by some numerical quadratures. Radial basis functions augmented with monomials are used in to create shape functions. These shape functions have delta function property. Also the time derivatives is eliminated by using two-step finite differences approximation. Two illustrative numerical examples are given to show the stability and accuracy of the present method. تفاصيل المقالة

In this paper, a novel and practical approach are proposed to solve the fuzzy optimal control (FOC) using an improved multi-layer perceptron (IMLP) network along with the Pontryagin minimum principle (PMP). Here, it is worthwhile to mention that in the fuzzy Hamilton function, instead of functions of control and trajectory and the Lagrange multipliers, the approximate solutions are replaced based on the IMLP neural network, which is a Three-layer type. تفاصيل المقالة

In this paper, first the Newton’s divided difference interpolation method based on the gH difference on fuzzy data is introduced. Then the numerical methods entitled fuzzy Euler and modified fuzzy Euler are used to solve fuzzy impulsive initial value problem. Moreover the algorithms for the fuzzy impulsive initial value problem are explained and their local truncation errors are obtained in details. Finally, for more illustration some numerical examples are solved. تفاصيل المقالة

In the present paper, we obtain the traveling wave fuzzy solution for the fuzzy linear Transport equation and the fuzzy Wave equation by considering the type of generalized Hukuhara differentiability. The d'Alembert's formulas for the fuzzy Wave equation obtained by Considering the type of gH-differentiability of the solution. Also, The existence and the uniqueness of these solutions and the stability of the fuzzy Wave equation are shown. تفاصيل المقالة

In this study, we develop an approximate formulation for two-dimensional (2D) Sobolev equations based on pseudospectral meshless radial point interpolation (PSMRPI). The Sobolev equations which are arisen in the fluid flow penetrating rocks, soils, or different viscous media do not have an exact solution except in some special cases. The problem can be rigorously solved particularly when the geometry of the domain is more complex. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. It is proved that the method is convergent and unconditionally stable in some sense with respect to the time. The main results of the Sobolev equation are demonstrated by some examples to show the validity and trustworthiness of the PSMRPI technique. تفاصيل المقالة

In this research paper, a numerical method is presented for solving second-order hybrid fuzzy differential equations by using fuzzy Taylor expansion under generalized Hukuhara differentiability and also with convergence theorem. Also, the method is illustrated by solving several numerical examples. The final results showed that the solution of the second-order hybrid fuzzy differential equations. تفاصيل المقالة

This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method ($ RKHSM $). Comparing the results of these methods as well as comparing the current method ($NSJOM$) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated. تفاصيل المقالة

The meshless local radial point interpolation (MLRPI) method is applied to examine the magnetohydrodynamic (MHD) ow of third grade uid in a porous medium. The uid saturates the porous space between the two boundaries. Several limiting cases of fundamental ows can be obtained as the special cases of present analysis. The variations of pertinent parameters are addressed. تفاصيل المقالة

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution of algebraic equations. تفاصيل المقالة

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎ تفاصيل المقالة

The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the excellence of this new method. So, we chose Emden-Fowler type differential equations and solved them utilizing this method. To confirm the accuracy of the new method and to show the preeminence of EOMs over OOMs, the norm 1 of the residual and error function for both methods are evaluated for multiple $m$ values, where $m$ is the degree of the Bernstein polynomials. We report the results by some plots to illustrate the error convergence of both methods to zero and also to show the primacy of the new method versus OOMs. The obtained results demonstrate the increased accuracy of the new ‎method.‎ تفاصيل المقالة