rational radial basis functions for solving ordinary differential equations

This paper presents an effective meshfree method for solving ordinary differential equations (odes) using rational radial basis functions (rrbfs). traditional radial basis function (rbf) methods suffer from ill-conditioning and difficulties in handling steep gradients or singularities. to address these issues, we explore the use of rational forms of rbfs, which exhibit improved numerical stability and higher accuracy near singularities or boundary layers. the method is tested on one ode with steep boundary layer. numerical results demonstrate that rrbfs provide superior accuracy, particularly in regions with steep fronts or sharp gradients.