Sinc-Galerkin method for solving nonlinear boundary-value problems
This paper deals with nonlinear ordinary differential equations of \(2m\)th-order \((m= 1,2,3)\), \[ u^{(2m)}+ r(x) uu'+ k(x) H(u)= f(x),\quad 0\leq x\leq 1, \] subject to the boundary conditions \(u^{(j)}(0)= 0\), \(u^{(j)}(1)= 0\), \(0\leq j\leq m-1\), where \(H(u)\) may be a polynomial or a rational function, or exponential. The authors illustrate how the sinc-Galerkin method may be used to replace our equation by an explicit system of nonlinear algebraic equations that is solved by Newton's method. Four numerical examples are presented.
scientific article; zbMATH DE number 2167471