Abstract
An adaptive spectral collocation method based on the parametric iteration method is established for simulating the solution of nonlinear initial value problems of ordinary differential equations. The implementation of the presented approach is demonstrated by solving several nonlinear problems. The numerical results obtained using the developed method are compared with those of the Matlab ode45 and ode87 solvers. This comparison shows that the developed algorithm is a promising tool to handle these kinds of problems.
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