In this paper, we obtain the solution of linear and nonlinear delay differential equations in reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for More
In this paper, we obtain the solution of linear and nonlinear delay differential equations in reproducing kernel space. For this purpose, regarding the equation and conditions governing it, a linear operator is defined and subsequently an orthonormal complete system for reproducing kernel space is obtained by using the adjoint operator and reproducing kernel function. Then, the solution of these equations is obtained in the form of a series of the basic functions. Indeed, the analytical solution is represented by infinite series, and the approximate solution is obtained by using an iterative method. As one of the main aims, the convergence analysis and error behavior are discussed for the proposed method. Finally, some numerical examples are studied to demonstrate the validity and applicability of the proposed method. The obtained results of the proposed method are compared with the exact solutions and the earlier works. The outcomes from numerical examples illustrate that the proposed method is very effective and convenient.
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In this paper‎, ‎we will present a new method for solving a class of two-dimensional linear Volterra integral equation of the second kind with weakly singular kernel from Abel type in the reproducing kernel space‎. The reproducing kernel function is discusse More
In this paper‎, ‎we will present a new method for solving a class of two-dimensional linear Volterra integral equation of the second kind with weakly singular kernel from Abel type in the reproducing kernel space‎. The reproducing kernel function is discussed in detail. Weak singularity of problem is removed by applying integration by parts. Further, improper integral belongs to L_2 (Ω). ‎In our method the exact solution ϕ(x,t) is represented in the form of series in the reproducing kernel space W(ω), and the approximate solution ϕ_n (x,t) is constructed via truncating the series to n terms. ‎Convergence analysis of the method is proved in detail‎. ‎Some numerical examples are also studied to demonstrate the efficiency and accuracy of the presented method‎. ‎The obtained results show that the error of the approximate solution is monotone decreasing in the sense of the norm of W(ω), when increasing the number of the nodes. Also, that indicate the method is simple and effective. It turns out that this method is valid.
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Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essenti More
Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear and complex the exact solution can usually not be calculated. So finding a numerical solution with high precision for these equations is essential. In this paper we present a numerical method based on the transferred Legendre polynomials to solve multiple pantograph delay differential equations. In this method we use the Legendre-Gauss-Lobato collocation points to discretize the problem and turn the problem into a nonlinear programming problem. From solving this nonlinear programming problem we get an approximate solution for the the main multiple pantograph delay differential equation. We analyse the feasibility of the nonlinear programming problem and the convergence of the obtained approximate solution to the exact solution. In addition by solving several numerical examples and comparing the method with other methodsWe show the efficiency and the capability of the proposed method.
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In this paper, we propose a feasible interior-point algorithm for mixed symmetric cone linear complementarity problems which are a general class of complementarity problems. The symmetrization of the search directions used in this paper is based on Nesterov and Todd sca More
In this paper, we propose a feasible interior-point algorithm for mixed symmetric cone linear complementarity problems which are a general class of complementarity problems. The symmetrization of the search directions used in this paper is based on Nesterov and Todd scaling scheme. By using Euclidean Jordan algebra, we prove the convergence analysis of the proposed algorithm and show that the complexity bound of the algorithm matches the currently best known iteration bound for feasible interior-point methods.
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تحقیق حاضر، تابع مجهول را بر اساس چند جمله ایهای مونتز- لژاندر نرمال شده تقریب می زند که مربوط به یک روش طیفی برای حل معادلات انتگرال فردهلم و ولترای غیرخطی است. در این روش، با استفاده از ماتریسهای عملیاتی یک دستگاه معادلات جبری بدست می آید که با استفاده از طرح نیوتن به More
تحقیق حاضر، تابع مجهول را بر اساس چند جمله ایهای مونتز- لژاندر نرمال شده تقریب می زند که مربوط به یک روش طیفی برای حل معادلات انتگرال فردهلم و ولترای غیرخطی است. در این روش، با استفاده از ماتریسهای عملیاتی یک دستگاه معادلات جبری بدست می آید که با استفاده از طرح نیوتن به راحتی می توان آن را حل کرد. پایداری، کران خطا و آنالیز همگرایی روش با ارائه چند قضیه به تفضیل مورد بحث قرار گرفته است. برای نشان دادن کارآیی روش پیشنهاد شده، چند مثال مشخص شده است.
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