Решение неоднородных дифференциально-алгебраических систем уравнений электрических цепей с помощью табличной записи уравнений и рядов Тейлора

Abstract

Previously known method of solving systems of linear ordinary differential equations using Taylor Series is adapted for solving non-linear equations and non-homogeneous equations with any right part. Specific feature of non-linear problems is solving of linear equations many times at each time step. Proposed approach takes into account this feature. New recurrence formulae suitable for solving systems of linear algebraic equations by iterational methods were derived. These methods, including Conjugate Gradient Method, effectively use sparsity of matrixes of the systems and also proximity of initial approximation to the solution. Table form of equations of electrical circuits is used because it is simple and universal. This form allows not form matrix of the system of equations in apparent avatar and saves computation work and time. Table form of system of equations gives easy possibility to transform initial differential-algebraic equations of electrical circuits to the system of ordinary differential equations in Cauchy form.