IN THIS REPORT ARE TWO TYPES OF MATRIX DIFFERENTIAL EQUATIONS. FIRST Built Numerical solution INITIAL VALUE PROBLEMS FOR MATRIX METHODS USING LINEAR MATRIX multi. BELOW, VIA LINEAR INTERPOLATION MATRIX SOLUTIONS Built number continues COTAS WITH ERROR EXPRESSED IN TERMS OF DATA. Particular attention is given to RICCATI TYPE EQUATIONS AND GENERALIZED Lyapunov WITH VARYING COEFFICIENTS. COUPLING SYSTEMS Partial differential equations (CONSIDERED MATRIX) ARE TREATED FOR THE CASE OF MIXED PROBLEMS (CONDITIONS TO INITIAL Contour). FIRST BUILDING IS ACCURATE SOLUTION IN THE FORM OF SERIES. Here TRUNC MATRIX OF THE SERIES IN A WAY THAT THE ERROR THIS DOMAIN ACOT ACOT UNIFORM PREFIX for an amount in advance.