This book is union for my scientific work it the time over more than fifty-five years. This is work in the mathematics and specialty mathematical modeling. In mathematics I introduced new approximated method: the conservative averaging method (CAM) and averaged integral spline. This CAM method after the modification fulfills energy conservation. In the case where we have multidimensional domain I formulate new class of the spline: this spline fulfills energy conservations. With my doctor students, we constructed spline on jump in the spline with function and its first differential approximation.
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