Nonpolynomial B-spline collocation method for solving singularly perturbed quasilinear Sobolev equation

سال انتشار: 1403
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 95

فایل این مقاله در 24 صفحه با فرمت PDF قابل دریافت می باشد

استخراج به نرم افزارهای پژوهشی:

لینک ثابت به این مقاله:

شناسه ملی سند علمی:

JR_IJNAO-14-30_001

تاریخ نمایه سازی: 17 شهریور 1403

چکیده مقاله:

In this paper, a singularly perturbed one-dimensional initial boundary value problem of a quasilinear Sobolev-type equation is presented. The nonlinear term of the problem is linearized by Newton’s linearization method. Time derivatives are discretized by implicit Euler’s method on nonuniform step size. A uniform trigonometric B-spline collocation method is used to treat the spatial variable. The convergence analysis of the scheme is proved, and the accuracy of the method is of order two in space and order one in time direction, respectively. To test the efficiency of the method, a model example is demonstrated. Results of the scheme are presented in tabular, and the figure indicates the scheme is uniformly convergent and has an initial layer at t = ۰.

نویسندگان

F. Edosa Merga

Department of Mathematics, Jimma University, Jimma, Oromia, Ethiopia.

G. File Duressa

Department of Mathematics, Jimma University, Jimma, Oromia, Ethiopia.

مراجع و منابع این مقاله:

لیست زیر مراجع و منابع استفاده شده در این مقاله را نمایش می دهد. این مراجع به صورت کاملا ماشینی و بر اساس هوش مصنوعی استخراج شده اند و لذا ممکن است دارای اشکالاتی باشند که به مرور زمان دقت استخراج این محتوا افزایش می یابد. مراجعی که مقالات مربوط به آنها در سیویلیکا نمایه شده و پیدا شده اند، به خود مقاله لینک شده اند :
  • Amiraliyev, G.M. and Amiraliyeva, I.G. Difference schemes for the sin-gularly ...
  • Amiraliyev, G.M., Duru, H. and Amiraliyeva, I.G. A parameter-uniform numerical ...
  • Amiraliyev, G.M. and Mamedov, Y.D. Difference schemes on the uni-form ...
  • Barenblatt, G.I., Zheltov, I.P. and Kochina, I.N. Basic concepts in ...
  • Chen, P.J. and Gurtin, M.E. On a theory of heat ...
  • Ciftci, I. and Halilov, H. Dependency of the solution of ...
  • Duressa, G.F. and Reddy, Y.N. Domain decomposition method for sin-gularly ...
  • Duru, H. Difference schemes for the singularly perturbed Sobolev periodic ...
  • Geng, F., Tang, Z. and Zhou, Y. Reproducing kernel method ...
  • Gunes, B. and Duru, H. A second-order difference scheme for ...
  • Huilgol, R.R. A second order fluid of the differential type, ...
  • Jiwari, R. Local radial basis function-finite difference based algorithms for ...
  • Jiwrai, R. and Mittal, R.C. A higher order numerical scheme ...
  • Jiwari, R., Singh, S. and Singh, P. Local RBF-FD-based mesh-free ...
  • Kadalbajoo, M.K. and Patidar, K.C. Singularly perturbed problems in partial ...
  • Kumar, N., Toprakseven, Ş. and Jiwari, R. A numerical method ...
  • Mohapatra, J. and Shakti, D. Numerical treatment for the solution ...
  • Nikolis, A. and Seimenis, I. Solving dynamical systems with cubic ...
  • Schoenberg, I.J. On trigonometric spline interpolation, J. math. mech. (۱۹۶۴), ...
  • Van Duijn, C.J., Fan, Y., Peletier, L.A. and Pop, I.S. ...
  • Vijayakumar, V., Udhayakumar, R. and Kavitha, K. On the approximate ...
  • Zahra, W.K. Trigonometric B-spline collocation method for solving PHI-four and ...
  • نمایش کامل مراجع