شماره ركورد كنفرانس :
1151
عنوان مقاله :
An adaptive meshfree method for nearly singular solutions of the KdV equations
عنوان به زبان ديگر :
An adaptive meshfree method for nearly singular solutions of the KdV equations
پديدآورندگان :
Garmanjani Gholamreza نويسنده , Esmaeilbeigi Mohsen نويسنده
كليدواژه :
KdV equation , Meshless method , Node adaptive , stability analysis , RBF collocation
عنوان كنفرانس :
دومين همايش ملي رياضيات و كاربردهاي آن
چكيده لاتين :
In this paper, we are interested in solving the one-dimensional nonlinear KdV equation, whose
solution presents rapid variations or high gradients in some local regions of the domain. The
radial basis function (RBF) collocation method is combined with the nite dierence scheme,
because, unlike with Kansaʹs method, nonlinear PDEs can be converted to a system of linear
equations, and a new adaptive algorithm is used to choose the location of the collocation
points in any time step. Also, numerical stability can be obtained for our scheme, using
the spectral norm of the amplication matrix. Results show that the method is capable of
reducing the number of nodes in the grid without compromising the accuracy of the solution
and the adaptive grading scheme is eective in localizing oscillations.
شماره مدرك كنفرانس :
4475081