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Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation. (English) Zbl 1122.65367
Summary: The Adam-Bashforth method and The Adam-Moulton method are two known multi-step methods for finding the numerical solution of the initial value problem of ordinary differential equation. These two methods use the Newton backward difference method to approximate the value of f(x,y) in the integral equation which is equivalent to the given differential equation.
MSC:
65L05Initial value problems for ODE (numerical methods)
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
45G10Nonsingular nonlinear integral equations
65R20Integral equations (numerical methods)