یک روش هم مکانی برای حل معادلات انتگرال ولترای نوع دوم غیرخطی از طریق جمله اول سری توابع والش

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی، دانشکده علوم، دانشگاه اراک، ایران، کدپستی 8349-8-38156

چکیده

دراین مقاله یک روش عددی برای حل معادلات انتگرال ولترای نوع دوم غیرخطی ارایه می شود. روش بر پایه

زیربازه با طول یکسان m تقریب تابع مجهول توسط تک جمله اول توابع والش بنا م ی گردد. در واقع بازه ( ٠, ١ ] به

تقسیم و در هر زیربازه تابع مجهول با جمله اول ازتوابع والش تقریب زده می شود. با استفاده از یک روش هم مکانی، ضرایب این تقریب ها به دست می آیند. بدین ترتیب یکتقریب بلاک-پالسبرای تابع مجهول حاصل می شود که می توان

با استفاده از آن، تقریب های پیوسته و همچنین نقطه واری را نیز به دست آورد. یک آنالیز همگرایی برای این تقریب های

پیوسته ارائه می گردد. نتایج عددی توانایی و دقت روش را تایید می کنند. این روش از نظر محاسباتی جذاب است و به

سادگی می توان آن را برای حل دستگاه های معادلات انتگرال ولترا نیز تعمیم داد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

A collocation method for solving nonlinear second kind Volterra integral equations through single-term Walsh series

نویسنده [English]

  • Behnam Sepehrian
Department of Mathematics, Arak University, Arak, Iran. P. O. Box 38156-8943.
چکیده [English]

In this paper, a numerical method for solving second kind nonlinear Volterra integral equations

is presented. The method is based upon the extension of unknown function by single term Walsh series.

Indeed, the interval [0, 1) is divided to m equal subinterval and in each interval, the unknown function is extended by the first term of Walsh series functions. By using a collocation method the coefficients of these extensions are computed and a block-pulse approximation of the unknown function is obtained. By the block-pulse approximation both continuous and pointwise approximations can be obtained. A convergence analysis for continuous approximations are investigated. The numerical examples confirm the ability and

accuracy of the method. The method is computationally attractive and can easily be generalized for the systems of nonlinear volterra equations.

کلیدواژه‌ها [English]

  • Collocation
  • Integral equation
  • Volterra
  • Walsh functions
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