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

A Computational investigation on the dynamics of shallow water waves

Paper presented at the 4th Strathmore International Mathematics Conference (SIMC 2017), 19 - 23 June 2017, Strathmore University, Nairobi, Kenya.The dynamics of shallow water waves has been an active research area for the past several decades. In this context, there are several models that govern this wave flow. In this study, finite element method based on B-spline interpolation functions are successfully applied to Korteweg-de Vries equation with power law nonlinearity to examine the motion of a single solitary wave whose analytical solution is known. The stability analysis is also carried out for these waves. Also, evolution of solitons is studied with Gaussian and undular bore initial conditions.Yalova University, Yalova 77100, Turke

Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation

In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and a priori error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable

An efficient approach to numerical study of the MRLW equation with b spline collocation method

A septic B-spline collocation method is implemented to find the numerical solution of the modified regularized long wave (MRLW) equation. Three test problems including the single soliton and interaction of two and three solitons are studied to validate the proposed method by calculating the error norms \u1d43f��2 and \u1d43f��∞ and the invariants \u1d43c��1, \u1d43c��2, and \u1d43c��3. Also, we have studied the Maxwellian initial condition pulse.The numerical results obtained by the method show that the present method is accurate and efficient. Results are compared with some earlier results given in the literature. A linear stability analysis of the method is also investigated

A new approach for numerical solution of modified korteweg-de vries equation

In this paper, a lumped Galerkin method is applied with cubic B-spline interpolation functions to find the numerical solution of the modified Korteweg-de Vries (mKdV) equation. Test problems including motion of single solitary wave, interaction of two solitons, interaction of three solitons, and evolution of solitons are solved to verify the proposed method by calculating the error norms L2 and L1 and the conserved quantities mass, momentum and energy. Applying the von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Consequently, the obtained results are found to be harmony with the some recent result

Numerical solutions of the Kawahara equation by the septic B spline collocation method

In this article, a numerical solution of the 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. The accuracy of the proposed method is checked by two test problems. L2 and L∞ error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results

Application of Petrov-Galerkin finite element methodto shallow water waves model: Modified Korteweg-deVries equation

In this article, modi ed Korteweg-de Vries (mKdV) equation is solved numerically by using lumped Petrov-Galerkin approach, where weight functions are quadratic and the element shape functions are cubic B-splines. The proposed numerical scheme is tested by applying four test problems including single solitary wave, interaction of two and three solitary waves, and evolution of solitons with the Gaussian initial condition. In order to show the performance of the algorithm, the error norms, L2, L1, and a couple of conserved quantities are computed. For the linear stability analysis of numerical algorithm, Fourier method is also investigated. As a result, the computed results show that the presented numerical scheme is a successful numerical technique for solving the mKdV equation. Therefore, the presented method is preferable to some recent numerical methods

Numerical Study of Rosenau-KdV Equation Using Finite Element Method Based on Collocation Approach

In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms L2 and L∞ are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves

Massive retroperitoneal tubercular abscess mimicking a leaking abdominal aortic aneurysm: a case report

In spite of being a common diagnosis in the patients of Asian origin, atypical presentations of tuberculosis may pose diagnostic challenges. We report a huge prevertebral abscess in a 30-year-old female, mimicking a leaking aortic aneurysm. The patient was managed successfully by emergency decompression and stabilization. The issues related to poor patient compliance to chemotherapy and management of atypical presentations of spinal tuberculosis are discussed here