Quadrature Formula with Five Nodes for Functions with a Boundary Layer Component

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• 作者：Alexander Zadorin (19)
  Nikita Zadorin (19)
  
• 关键词：function ; numerical integration ; boundary layer component ; nonpolynomial interpolation ; quadrature rule ; uniform accuracy
• 刊名：Lecture Notes in Computer Science
• 出版年：2013
• 出版时间：2013
• 年：2013
• 卷：8236
• 期：1
• 页码：547-554
• 全文大小：146KB
• 参考文献：1. Berezin, I.S., Zhidkov, N.P.: Computing Methods. Nauka, Moskow (1966) (in Russian)
  2. Bakhvalov, N.S.: Numerical Methods. Nauka, Moskow (1975) (in Russian)
  3. Zadorin, A.I., Zadorin, N.A.: Quadrature formulas for functions with a boundary-layer component. Comput. Math. Math. Phys.聽51(11), 1837鈥?846 (2011) 10.1134/S0965542511110157">CrossRef
  4. Miller, J.J.H., O鈥橰iordan, E., Shishkin, G.I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific, Singapore (1996)
  5. Zadorin, A.I.: Method of interpolation for a boundary layer problem. Sib. J. of Numer. Math.聽10(3), 267鈥?75 (2007) (in Russian)
  6. Zadorin, A.I.: Interpolation Method for a Function with a Singular Component. In: Margenov, S., Vulkov, L.G., Wa艣niewski, J. (eds.) NAA 2008. LNCS, vol.聽5434, pp. 612鈥?19. Springer, Heidelberg (2009) 10.1007/978-3-642-00464-3_72">CrossRef
  7. Zadorin, A.I., Zadorin, N.A.: Spline interpolation on a uniform grid for functions with a boundary-layer component. Comput. Math. Math. Phys.聽50(2), 211鈥?23 (2010) 10.1134/S0965542510020028">CrossRef
  8. Zadorin, A.I.: Spline interpolation of functions with a boundary layer component. Int. J. Numer. Anal. Model., series B聽2(2-3), 562鈥?79 (2011)
  9. Vulkov, L.G., Zadorin, A.I.,: Two-grid algorithms for an ordinary second order equation with exponential boundary layer in the solution. Int. J. Numer. Anal. Model.聽7(3), 580鈥?92 (2010)
  10. Dahlquist, G., Bjorck, A.: Numerical Methods in Scientific Computing, vol.聽1. SIAM, Philadelphia (2008) 10.1137/1.9780898717785">CrossRef
  
• 作者单位：Alexander Zadorin (19)
  Nikita Zadorin (19)
  
  19. Omsk Filial of Sobolev Mathematics Institute SB RAS, Pevtsova 13, Omsk, 644099, Russia
  
• ISSN：1611-3349

文摘

Quadrature formula for one variable functions with a boundary layer component is constructed and studied. It is assumed that the integrand can be represented as a sum of regular and boundary layer components. The boundary layer component has high gradients, therefore an application of Newton-Cotes quadrature formulas leads to large errors. An analogue of Newton-Cotes rule with five nodes is constructed. The error of the constructed formula does not depend on gradients of the boundary layer component. Results of numerical experiments are presented.