Evaluation of analytic functions by generalized digital integration

An integral of Haar functions yields triangular waveforms at subintervals where the Haar functions initially exist. These waveforms can be expressed by Haar series. Coefficients of their series can be given in quasi binary numbers. If the solutions of ordinary differential equations(ODE) are expressed by Haar series with unknown coefficients, given ODE can be written in a Haar function system by using Haar coefficients for the triangular waveforms and variable coefficients of the ODE. They are given in terms of matrix equations. Unknown Haar coefficients can be determined by solving such matrix equations. Haar approximations of their solutions can be obtained through a consistent procedure of computation.