Abstract
This work develops formulas for numerical integration with spline interpolation. The new formulas are shown to be alternatives to the Newton–Cotes integration formulas. These methods have important application in integration of tables or for discrete functions with constant steps. An error analysis of the technique was conducted. A new type of spline interpolation is proposed in which a polynomial passes through more than two tabulated points. The results show that the proposed formulas for numerical integration methods have high precision and absolute stability. The obtained methods can be used for the integration of stiff equations. This paper opens a new field of research on numerical integration formulas using splines.
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