Numerical Solution of Nonlinear Initial Value Problem on its Interval of Existence

In general, the computational and numerical methods available in the literature for solving nonlinear differential equations with initial conditions provide only the local existence of the solution.In this work, we present a computational and numerical method for computing the solution for first-order nonlinear differential equations with initial conditions on its entire interval of existence.The interval of existence is guaranteed by upper and lower solutions and/or coupled lower and upper solutions.In this work, we have used the generalized quasilinearization method to construct our numerical and computational methods to compute the solution on its entire interval of existence.As an example, we have presented various numerical results relating to the Ricatti type of differential equations.Our work also includes examples from biological models, such as the logistic equation where the interval of existence is [0, ).