Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Engineering and applied mathematics disciplines that involve differential equations in general, initial value problems particular, include classical mechanics, thermodynamics, electromagnetism, the general theory of relativity. A reliable, stable, efficient, consistent numerical scheme is frequently required for modelling simulation a wide range real-world using equations. In this study, tangent slope assumed to be contra-harmonic mean, which arithmetic mean used as correction instead Euler’s method improve efficiency improved technique solving ordinary with conditions. The stability, consistency, system were evaluated, conclusions supported by presentation test applications engineering. According stability analysis, proposed has wider region than other well-known methods are currently literature initial-value problems. To validate rate convergence technique, few both scalar vector valued types examined. method, modified Euler explicit known have all been calculate absolute maximum error, error at last grid point integration interval under consideration, computational time seconds performance. Lorentz was an example illustrate validity solution provided newly developed method. determined more reliable commonly existing same order convergence, mentioned calculations visualization results produced discussed, Mat Lab-R2011b used.