Abstract
This paper presents a half step numerical method for solving directly general second order initial value problems. The scheme is developed via collocation and interpolation technique invoked on power series polynomial. The proposed method is consistent, zero stable, order four and three. This method can estimate the approximate solution at both step and off step points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed scheme over some existing schemes of same and higher order.
Highlights
There are many 1-D optimum path problems existing in universal and diary life
This paper aims to set up relationship between the 1-D optimum path problem and the “Principle of Minimum
The optimum path problem of 1-D two end-points A and B fixed is reduced to an optimum of an vector integral equation of Fredholm type, i.e
Summary
There are many 1-D (one dimension) optimum path problems existing in universal and diary life. Optimum path in logistics navigation, optimum path in military design-attacking target, optimum path in wind moving track, and typhoon track, etc. The 1-D optimum path problem with constraint(s), usually, it can be changed to un-constraint problem by method of Lagrange multipliers [3]. The optimum problem of integrand with given scalar function have been summery in mathematical hand books, e.g., [4]. There are many principles on energy relating to mechanical problems or relating to scientific problems. These principles have no connection with the optimum path problem
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