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لا صخلم ثحبلا اذه يف ءوضلا طلسن ىلإ جنر قرط ضعب – لضفلا دوعي يذلاو ةديدجلا اتك يف هداجيإ ىلإ ءاملعلا نم لاك [David and Olin] ثيح نأ قرطلا هذه ةزيم اهنإ بلطتت ةلادلل نيمييقت طقف f ذ قرطلل ةبسنلاب ل تامييقت ثلاثو ةثلاثلا ةبترلا تا f قرطلل ةبسنلاب ةعبارلا ةبترلا تاذ ، امإ ةسماخلا ةبترلا تاذ قرطلا اهنإف بلطتت عبرأ ل تامييقت f ، نيح يف نإ ل تامييقت بلطتت ةيدايتعلاا قرطلا f رثكأ نم كلذ . ىلع اءانبو لا دعلا قرطلا هذهل ةديدجلا ةزيم نم قرطلا هذه لمع نيسحتب انمق دقف ةيد للاخ ةفاضإ لا دح <1 γ ,0< ∞ → n , 0 → h as 0 1 ⇒ − = ∆ + n n y y γ γ قرطلا هذه ىلإ ح يف اهتعرسو قرطلا هذه لمع ةقد ةدايز ىدم ىلإ ريشت اهيلع انلصح يتلا جئاتنلا تناكف ل تلاداعملا . Abstract In this paper we modify some sort of Runge-Kutta methods developed by David and Olin which need less function evaluation than ordinary corresponding Runge-Kutta methods. We improve the stability region of these methods by adding a suitable term for the formulas of the methods. We have shown these improvements theoretically and practically.

Modifying Runge – Kutta methods with higher order derivative approximations