A whole category of engineering and economic problems can be reduced to solving a set of differential equations. Downsides of known approaches for their solutions include limited accuracy numerical methods with stringent requirements for computational power. A direct analytical solution should be derived to eliminate such flaws. This research intends to derive such a solution for an n-dimensional set of recurrence relations for first-order differential equations, linearly dependent on the right side. The research methodology relies on successive integration of the considered set in view of the initial conditions. The overall solution was derived as a sum of products of exponential multipliers with constant coefficients that are defined through weights of a tree graph, which is a descriptor of successive integration. An analytical solution for an n-dimensional set of recurrent differential equations in view of the initial conditions has been derived for the first time in this research.
The article discusses the prospects for using various types of renewable energy sources for continental climate conditions (on the example of the Zabaikalye Territory). It is determined that the most efficient is the use of solar energy for the heating needs. The method for optimizing the composition of the equipment in combined heating systems, which allows quick determination of the optimal amount of solar collectors without reusability of complex astronomical calculations needed to determine the exact position of the Sun in the required time. Application of the developed methodology in conducting energy audit of heating supply objects can reasonably represent the technical and economic advice on the implementation of renewable energy sources.
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