Numerical solutions of the modified KdV Equation with collocation method

In this article, numerical solutions of the modified Korteweg-de Vries (MKdV) equation have been obtained by a numerical technique attributed on collocation method using quintic B-spline finite elements. The suggested numerical scheme is controlled by applying three test problems involving single solitary wave, interaction of two and three solitary waves. To check the performance of the newly applied method, the error norms, L2 and L∞, as well as the three lowest invariants, I1, I2 and I3, have been calculated. The acquired numerical results are compared with some of those available in the literature. Linear stability analysis of the algorithm is also examined

A quartic subdomain finite element method for the modified kdv equation

In this article, we have obtained numerical solutions of the modified Korteweg-de Vries (MKdV) equation by a numerical technique attributed on subdomain finite element method using quartic B-splines. The proposed numerical algorithm is controlled by applying three test problems including single solitary wave, interaction of two and three solitary waves. To inspect the performance of the newly applied method, the error norms, L2 and L∞, as well as the four lowest invariants, I1, I2, I3 and I4 have been computed. Linear stability analysis of the algorithm is also examined

A detailed numerical study on generalized ROSENAU-KDV equation with finite element method

In this study, we have got numerical solutions of the generalized RosenauKdV equation by using collocation finite element method in which septic B-splines are used as approximate functions. Effectivity and proficiency of the method are shown by solving the equation with different initial and boundary conditions. Also, to do this L and L 2 error norms and two lowest invariants MI and EI have been computed. A linear stability analysis indicates that our algorithm, based on a Crank Nicolson approximation in time, is unconditionally stable. An error analysis of the new algorithm has been made. The obtained numerical solutions are compared with some earlier studies. This comparison clearly indicates that the obtained results are better than the earlier results

A new numerical application of the generalized Rosenau-RLW equation

. This study implemented a collocation nite element method based on septic B-splines as a tool to obtain the numerical solutions of the nonlinear generalized RosenauRLW equation. One of the advantages of this method is that when the bases are chosen at a high degree, better numerical solutions are obtained. E ectiveness of the method is demonstrated by solving the equation with various initial and boundary conditions. Further, in order to detect the performance of the method, L2 and L1 error norms and two lowest invariants IM and IE were computed. The obtained numerical results were compared with some of those in the literature for similar parameters. This comparison clearly shows that the obtained results are better than and in good conformity with some of the earlier results. Stability analysis demonstrates that the proposed algorithm, based on a Crank Nicolson approximation in time, is unconditionally stable

Bazı sığ su dalga denklemlerinin sonlu elemanlar yöntemi ile sayısal çözümleri

Altı bölümden olu¸san bu doktora tez çalı¸smasında, B-spline yaklaşım fonksiyonlarına bağlı sonlu elemanlar yöntemleri kullanılarak bazı sığ su dalga denklemlerinin sayısal çözümleri üzerinde çalışılmıştır. Elde edilen sayısal sonuçlar literatürde yer alan teorik ve diger sayısal sonuçlarla karşılaştırılmıştır

Kollokasyon sonlu eleman yöntemi ile mkdv denkleminin sayısal çözümleri

Bu çalışmada, modifiye edilmiş Korteweg-de Vries (mKdV) denkleminin sayısal çözümleri septik B-spline kollokasyon sonlu eleman yöntemi kullanılarak elde edilmiştir. Önerilen sayısal algoritmanın doğruluğu, tek soliton dalga, iki ve üç soliton dalganın girişimi gibi üç test probleminin uygulanması ile kontrol edilmiştir. Zamana bağlı Crank Nicolson yaklaşımına dayanan sayısal algoritmamız şartsız olarak kararlıdır. Yeni uygulanan yöntemin performansını kontrol etmek için, \u1d43f��2 , \u1d43f��∞ hata normları ile \u1d43c��1, \u1d43c��2, \u1d43c��3 ve \u1d43c��4 değişmezlerinin değerleri hesaplanmıştır. Elde edilen sayısal sonuçlar literatürde bulunan diğer sonuçlarla karşılaştırılmıştır

A numerical solution of the MEW equaiton using sextic B splines

In this article, a numerical solution of the modified equal width wave (MEW) equation, based on subdomain method using sextic B-spline is used to simulate the motion of single solitary wave and interaction of two solitary waves. The three invariants of the motion are calculated to determine the conservation properties of the system. L2 and L∞ error norms are used to measure differences between the analytical and numerical solutions. The obtained results are compared with some published numerical solutions. A linear stability analysis of the scheme is also investigate

Subdomain finite element method with quartic B-splines for the modified equal width wave equation

In this paper, a numerical solution of the modified equal width wave (MEW) equation, has been obtained by a numerical technique based on Subdomain finite element method with quartic Bsplines. Test problems including the motion of a single solitary wave and interaction of two solitary waves are studied to validate the suggested method. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and error norms L2 and L∞. A linear stability analysis based on a Fourier method shows that the numerical scheme is unconditionally stable

A numerical technique based on collocation method for solving modified Kawahara equation

In this article, a numerical solution of the modified Kawahara equation is presented by septic B-spline collocation method. Applying the von-Neumann stability analysis, the present method is shown to be unconditionally stable. L 2 and L ∞ error norms and conserved quantities are given at selected times. The accuracy of the proposed method is checked by test problems including motion of the single solitary wave, interaction of solitary waves and evolution of solitons

Solitary-wave solutions of the GRLW equation using septic B-spline collocation method

In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different lin- earization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L 2 and L ∞ and the invari- ants I 1 , I 2 and I 3 . A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numer- ical scheme is preferable to some recent numerical schemes