Abstract
In this Paper, we have derived the numerical integration formula for unequal data spacing. For doing so we use Newton’s Divided difference formula to evaluate general quadrature formula and then generate Trapezoidal and Simpson’s rules for the unequal data spacing with error terms. Finally we use numerical examples to compare the numerical results with analytical results and the well-known Monte- Carlo integration results and find excellent agreement.
Highlights
Numerical integration is the process of computing the value of a definite integral from a set of numerical values of the integrand
We use Newton’s Divided difference formula to derive the formula for unequal data spacing with the error term and use numerical examples to compare our solution with the exact solution and the well-known Monte – Carlo integration result
Using (1) into the integral we get,. This is the equation of general quadrature formula for unequal spacing
Summary
Numerical integration is the process of computing the value of a definite integral from a set of numerical values of the integrand. The basic problem in numerical integration [3,4,5] is to compute an approximate value of a definite integral to a given accuracy. If is a smooth function integrand over a small number of dimensions and the domain of integration is bounded, there are many methods for approximating the integral to the desired precision numerically. Method like Monte – Carlo [8] integration used random numbers over the interval to approximate the integral where the spaces between two points are not equal. We use Newton’s Divided difference formula to derive the formula for unequal data spacing with the error term and use numerical examples to compare our solution with the exact solution and the well-known Monte – Carlo integration result.
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