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Two Compact Techniques for Numerical Solution of the Klein-Gordon Equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مهر 1405 اصل مقاله (1.04 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.69408.3418 | ||
| نویسندگان | ||
| Emre Kırlı1؛ Dursun Irk2؛ Melis Zorsahin* 2 | ||
| 1Department of Mathematics, Aksaray University, 68100, Aksaray, Türkiye. | ||
| 2Department of Mathematics and Computer Sciences, Eskisehir Osmangazi University, 26040, Eskisehir, Türkiye. | ||
| چکیده | ||
| In this study, two compact numerical techniques are proposed for solving the nonlinear Klein-Gordon equation (KGE). The first method, denoted as $M_{1}$, combines the cubic B-spline collocation method with the Crank-Nicolson (CN) time integration scheme to provide a fully discrete formulation. The second method, referred to as $M_{2}$, employs a fourth-order accurate spatial discretization based on cubic B-spline basis functions, along with a one-step implicit time integration scheme of fourth-order accuracy. Consequently, the$M_{1}$ and $M_{2}$ methods achieve second- and fourth-order accuracy in both space and time, respectively. To assess the accuracy and efficiency of the proposed techniques, two benchmark test problems are considered. The $L_{\infty }$ error norms, along with spatial and temporal convergence rates, are computed. The numerical results confirm that the observed convergence rates closely match the theoretical predictions. Overall, the findings demonstrate that both methods are effective, with the $M_{2}$ technique exhibiting superior accuracy compared to existing approaches. | ||
| کلیدواژه‌ها | ||
| Cubic B-spline؛ Klein-Gordon equation؛ Collocation method؛ Finite Element | ||
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آمار تعداد مشاهده مقاله: 2 تعداد دریافت فایل اصل مقاله: 2 |
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