Numerical solution of a highly order linear and nonlinear equations using integrated radial basis function network method
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Keywords:
IRBFN, NEPAbstract
In this work, we examine a variety of regimes of dynamicitygenerated using means of a single partial differential equation of sixth order nonlinearity), the NEP equationand equation (a single linear partial differential equation of sixth order) making use of the integrated radial basis function network method, a more sophisticated numerical technique (IRBFN). Previously, we used the Galerkin
approach to generate NEP equation spinning solutions in one step. Firstly, we use the approach to replicate the previously found spinning regimes by solving the NEP equation. In the most recent round of numerical tests, we discover regimes that resemble whirling sequences of bends with one kink, two, or threeeach. Analysis is done on the changes in the distance between the kinks. Boundary conditions of two types are taken into consideration: periodic and homogenous. It is investigated how the dynamics rely on the domain’s size and how bigger domains can support more spinning fronts. The kinks’ direction of motion is determined by the initial state, but not their sizes or velocities. Secondly, We solve the Nikolaevskiy equation as an example for linear single partial differential equationusing IRBFN approach.
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