A collocation spectral method for two-dimensional Sobolev equations

• الحاوية / القاعدة: Boundary Value Problems
• المؤلفون الرئيسيون: Shiju Jin, Zhendong Luo
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: SpringerOpen 2018-05-01
• الموضوعات: Collocation spectral method; Sobolev equation; Existence and stability as well as convergence; Numerical experiment
• الوصول للمادة أونلاين: http://link.springer.com/article/10.1186/s13661-018-1004-0
• تدمد: 1687-2770

Abstract This article mainly studies a collocation spectral method for two-dimensional (2D) Sobolev equations. To this end, a collocation spectral model based on the Chebyshev polynomials for the 2D Sobolev equations is first established. And then, the existence, uniqueness, stability, and convergence of the collocation spectral numerical solutions are discussed. Finally, some numerical experiments are provided to verify the corrections of theoretical results. This implies that the collocation spectral model is very effective for solving the 2D Sobolev equations.