Ordinary differential equation

دسترسی آزاد مقاله

1 - روش‌های عددی همتافته و متقارن برای حل عددی برخی مدل‌های ریاضی اجرام سماوی
علی عبدی سید احمد حسینی

 در سالهای اخیر، تئوری روشهای عددی برای دستگاه معادلات دیفرانسیل سخت و غیرسخت به یک کمال خاصی رسیده است. بنابراین، کدهای فوق‌العاده زیادی که بر پایه روش‌های رانگ-کوتا، روش‌های چندگامی خطی، روش‌های ابرشکف، روش‌های پیوندی یا روش‌های خطی عمومی هستند، وجود دا چکیده کامل

 در سالهای اخیر، تئوری روشهای عددی برای دستگاه معادلات دیفرانسیل سخت و غیرسخت به یک کمال خاصی رسیده است. بنابراین، کدهای فوق‌العاده زیادی که بر پایه روش‌های رانگ-کوتا، روش‌های چندگامی خطی، روش‌های ابرشکف، روش‌های پیوندی یا روش‌های خطی عمومی هستند، وجود دارند. اگرچه این روشها دارای دقت خوب و خواص پایداری مطلوب مانند A-پایداری و L-پایداری هستند، ولی برای حل عددی دسته‌های خاصی از مسایل که از زمینههای تحقیقاتی مختلفی ناشی میشوند، مناسب نیستند. برای مثال، مدل‌های ریاضی حرکت اجرام سماوی که دستگاه هامیلتونی هستند. از آنجایی که جواب چنین مسایلی دارای خواص هندسی خاصی از جمله همتافتگی و عموماً برگشتپذیری است، طبیعی است بهدنبال روشهایی باشیم که دارای این ویژگیها باشند. هدف این مقاله طراحی روشهای عددی همتافته و متقارن از مراتب بالا است. کارایی و دقت روشهای معرفی شده با نتایج عددی حاصل از پیادهسازی آنها روی مسایل هامیلتونی معروف از حرکت اجرام سماوی، تأیید خواهند شد. پرونده مقاله

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2 - Solving Volterra Integral Equations of the Second Kind with Convolution ‎Kernel‎
M. S. Barikbin A. R. Vahidi T. ِDamercheli

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad &lrm;et al., &lrm;&lrm;[K. Maleknejad &lrm;and Aghazadeh, Numerical solution of Volterr چکیده کامل

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad &lrm;et al., &lrm;&lrm;[K. Maleknejad &lrm;and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, &lrm;Appl. Math. Comput.&lrm; (2005)]&lrm; to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad &lrm;et al. &lrm;[K. Maleknejad &lrm;and&lrm; T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, &lrm;Indian J. Pure Appl. Math.&lrm; (2014)] &lrm;to gain the approximate solutions of systems of second kind Volterra integral equations with the help of Taylor expansion method. The Taylor expansion method transforms the integral equation into a linear ordinary differential equation (ODE) which, in this case, requires specified boundary conditions. Boundary conditions can be determined using the integration technique instead of differentiation technique. This method is more stable than derivative method and can be implemented to obtain an approximate solution of the Volterra integral equation with smooth and weakly singular kernels. An error analysis for the method is provided. A comparison between our obtained results and the previous results is made which shows that the suggested method is accurate enough and more &lrm;stable.&lrm; پرونده مقاله

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3 - Approximate solution of fourth order differential equation in Neumann problem
J. Rashidinia D. Kalvand L. Tepoyan

Generalized solution on Neumann problem of the fourth order ordinary differentialequation in space $W^2_\alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when thesolution is in classical form. Formulation of Quintic Spline Function has been derived and t چکیده کامل

Generalized solution on Neumann problem of the fourth order ordinary differentialequation in space $W^2_\alpha(0,b)$ has been discussed, we obtain the condition on B.V.P when thesolution is in classical form. Formulation of Quintic Spline Function has been derived and theconsistency relations are given.Numerical method,based on Quintic spline approximation hasbeen developed. Spline solution of the given problem has been considered for a certain valueof $\alpha$. Error analysis of the spline method is given and it has been tested by an example. پرونده مقاله

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4 - Numerical Solution of Nonlinear System of Ordinary Differential Equations by the Newton-Taylor Polynomial and Extrapolation with Application from a Corona Virus Model
Bahman Babayar-Razlighi

10.30495/ijm2c.2021.685126

In this paper, we consider a nonlinear non autonomous system of differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positi چکیده کامل

In this paper, we consider a nonlinear non autonomous system of differential equations. We linearize this system by the Newton's method and obtain a sequence of linear systems of ODE. We are going to solve this system on [0,Nl] , for some positive integer N and a positive real l>0 . For this purpose, in the first step we solve the problem on [0,l]. By knowing the solution on [0,l], we solve the problem on [l,2l] and obtain the solution on [0,2l]. We continue this procedure until [0,Nl]. In each partial interval [(k-1)l,kl], first of all, we solve the problem by the extrapolation method and obtain an initial guess for the Newton-Taylor polynomial solutions. These procedures cause that the errors don’t propagate. The sequence of linear systems in Newton's method are solved by a famous method called Taylor polynomial solutions, which have a good accuracy for linear systems of ODE. Finally, we give a mathematical model of the novel corona virus disease and illustrate accuracy and applicability of the method by some examples from this model and compare them by similar work, that simulate the numerical solutions. پرونده مقاله

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5 - APPLICATION NEURAL NETWORK TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS
Nouredin Parandin Somayeh Ezadi

In this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. In proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimi چکیده کامل

In this paper, we introduce a hybrid approach based on neural network and optimization teqnique to solve ordinary differential equation. In proposed model we use heyperbolic secont transformation function in hiden layer of neural network part and bfgs teqnique in optimization part. In comparison with existing similar neural networks proposed model provides solutions with high accuracy. Numerical examples with simulation results illustrate the effectiveness of the proposed model. پرونده مقاله

فهرست مقالات Ordinary differential equation

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