In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to combine DBFs and high order geometric numerical integrator for solving such a nonlinear partial differential equation (PDE) which preserves conservation laws. To demonstrate the performance of the proposed method we consider five test problems. We reckon [Formula: see text], [Formula: see text] and root mean square (RMS) errors and compare them with other results available in the literature. Besides the errors, we also monitor conservation laws of the KDV equation and we show that the method in this paper produces accurate results and preserves the conservation laws quite good. Numerical outcomes show that the present novel method is efficient and reliable for PDEs.
The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms.
Using the fiber bundle M over a manifold B, we define a semi-tensor (pull-back) bundle tB of type (p,q). The present paper is devoted to some results concerning with the vertical and complete lifts of some tensor fields from manifold B to its semi-tensor bundle tB of type (p,q).
The goal of the present paper is to analyze sharp type inequalities including
the scalar and Ricci curvatures of slant submersions in complex space forms.
The goal of the present paper is to analyze some geometric features of Clairaut pointwise slant submersions whose total manifold is a locally product Riemannian manifold. We describe Clairaut pointwise slant submersions from locally product Riemannian manifold onto a Riemannian manifold. We study pointwise slant submersions by providing a consequent which defines the geodesics on the total space of this type submersions. We also give a non-trivial example of the Clairaut pointwise slant submersions whose total manifolds are locally product Riemannian.
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