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Browsing Department of Mathematics by Author "AL- OMAİRİ, Salim Mahmood Yaseen"
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Item LINEARLY IMPLICIT SCHEMES FOR THE ROSENAU-KORTEWED-DE VRIES REGULARIZED LONG WAVE EQUATIONS(2015-06-25) AL- OMAİRİ, Salim Mahmood Yaseen; AYDIN, AyhanIn this thesis, we consider the numerical solution of the Rosenau– Korteweg de Vries– Reularized Long Wave (Rosenau KdV–RLW) equation which couples the general Rosenau–KdV and Rosenau–RLW equations. Two conserved quantities of the Rose nau KdV–RLW equation has been proven, namely the mass and the energy. The aim is to develop numerical methods to preserve these conserved quantities exactly or preserve with a small error. Two linearly implicit schemes for the initial–boundary value problem of the Rosenau KdV–RLW equation are proposed. One method is con servative and the other method is nonconservative. It is proved that the conservative method preserves the energy of the equation exactly. It is also shown that the scheme is second order accurate and unconditionally stable. The second scheme is nonconser vative. It is first order accurate and conditionally stable. Numerical results shown that both scheme well simulates the solitary wave of the equation in long time. Moreover, numerical results verify the exact energy conservation of the conservative scheme.