Convergence Analysis and Numerical Solutions of the Fisher's and Benjamin-Bono Equations by Operator Splitting Method - Zürnacı, Fatma; Tanoğlu, Gamze (Izmir Institute of Technology, 2014)
This thesis is concerned with the operator splitting method for the Fisher’s and Benjamin-Bono-Mahony type equations. We showthat the correct convergence rates inHs(R) space for Lie- Trotter and Strang splitting method which are obtained for these equations. In the proofs, the new framework originally introduced in (Holden, Lubich, and Risebro, 2013) is used. Numerical quadratures and Peano Kernel theorem, which is followed by the differentiation in Banach space are discussed In addition, we discuss the Sobolev space Hs(R) and give several properties of this space. With the help of these subjects, we derive error bounds for the first and second order splitting methods. Finally, we numerically check the convergence rates for the time step ∆t.
Fisher ve Benjamin-bono-mahony Denklemlerinin Operatör Ayırma Metodu ile Yakınsallık Analizi ve Nümerik Çözümleri
Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2014
Includes bibliographical references (leaves: 71-74)
Text in English; Abstract: Turkish and English
ix, 87 leaves
Keywords: Operator equation; Numerical solutions; Numerical analysis