In this paper, we solved the Newell-Whitehead equation approximately using Adomain Decomposition method and we have compared this solution with the exact solution; we found that the solution of this method is so close to the exact solution and this solution is slower to converge to the exact solution when we increase t however, this method is effective for this kind of problems.

In this article, the application of variational homotopy perturbation method is applied to solve Benjamin-Bona-Mahony equation. Then, we obtain the numerical solution of BBM equation using the initial condition. Comparison with Adomian's decomposition method, homotopy perturbation method, and with the exact solution shows that VHPM is more effective and accurate than ADM and HPM, and is reliable and manageable for this type of equation.

No abstract

In this paper, we study three types of finite difference methods, to find the numerical solution of reaction difference systems of PDEs in two dimensions. These methods are ADE, ADI and Hopscotch, where Gray-Scott model in two dimensions has been considered. Our numerical results show that the ADI method produces more accurate and stable solution than ADE method and Hopscotch method is the best because does not involve any tridiagonal matrix. Also we studied the consistency, stability and convergence of the above methods. Keywords: Gray-Scott model in two dimensions, finite difference methods, Alternating direction explicit method, Alternating direction implicit method, Hopscotch method. ‫بعدين‬ ‫في‬ ‫التفاعلي‬ ‫االنتشار‬ ‫لنظام‬ ‫المنتهية‬ ‫الفروقات‬ ‫حلول‬ ‫ائق‬ ‫طر‬ ‫مقارنة‬‫البياتي‬ ‫يونس‬ ‫عباس‬ 1 ‫مناع‬ ‫عبدهللا‬ ‫سعد‬ 2 ‫الرو‬ ‫امين‬ ‫محمد‬ ‫عبدالغفور‬ ‫ژ‬ ‫بياني‬ 3 1,3 ‫اق‬ ‫الموصل/العر‬ ‫ياضيات/جامعة‬ ‫الر‬ ‫و‬ ‫الحاسوب‬ ‫علوم‬ ‫كلية‬ 2 ‫اق‬ ‫اخو/العر‬ ‫ز‬ ‫العلوم/جامعة‬ ‫كلية‬ ‫البحث:‬ ‫استالم‬ ‫تاريخ‬ 23 / 4 / 2007 ‫البحث:‬ ‫قبول‬ ‫تاريخ‬ 15 / 8 / 200 ‫الملخص‬ ‫ف‬ ‫ي‬ ‫البحث‬ ‫هذا‬ ‫المنتهية‬ ‫الفروقات‬ ‫طرق‬ ‫من‬ ‫اع‬ ‫أنو‬ ‫ثالث‬ ‫ندرس‬ ، ‫وبالتفصيل‬ ، ‫ان‬ ‫م‬ ‫اام‬ ‫لنظ‬ ‫العددي‬ ‫الحل‬ ‫إليجاد‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ن،‬ ‫اد‬ ‫ا‬ ‫ع‬ ‫اي‬ ‫ا‬ ‫ف‬ ‫ااف‬ ‫ا‬ ‫الم‬ ‫اي‬ ‫ا‬ ‫و‬ ‫ال‬ ‫اوع‬ ‫ا‬ ‫ن‬ ‫ان‬ ‫ا‬ ‫م‬ ‫اة‬ ‫ا‬ ‫النوي‬ ‫ار‬ ‫ا‬ ‫خي‬ ‫اة‬ ‫ا‬ ‫غي‬ ‫الج‬ ‫الية‬ ‫ا‬ ‫التفاض‬ ‫ت‬ ‫ااد‬ ‫ا‬ ‫المع‬ ‫ذ‬ ‫اات‬ ‫ا‬ ‫المتجه‬ ‫اة‬ ‫ا‬ ‫ي‬ ‫طر‬ ‫اي‬ ‫ا‬ ‫ه‬ ‫ارق‬ ‫ا‬ ‫الو‬ ‫ه‬ ‫يحة‬ ‫ار‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫الص‬ ‫اة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫المتعاقب‬ ADE ‫امنية‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ال‬ ‫اة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫المتعاقب‬ ‫اات‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫المتجه‬ ‫اة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ي‬ ‫وطر‬ ) (ADI) ‫و‬ ‫اة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ي‬ ‫طر‬ Hopscotch ‫او‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫لنم‬ ) Gray-Scott ‫اء‬ ‫ف‬ ‫في‬ ‫منية‬ ‫ال‬ ‫المتعاقبة‬ ‫المتجهات‬ ‫ة‬ ‫ي‬ ‫طر‬ ‫أن‬ ‫العددية‬ ‫النتاغج‬ ‫من‬ ‫استنتجنا‬ ‫و‬ ‫ن.‬ ‫عد‬ ‫ات‬ ADI ) ‫يحة‬ ‫ار‬ ‫ا‬ ‫الص‬ ‫اة‬ ‫ا‬ ‫المتعاقب‬ ‫اات‬ ‫ا‬ ‫المتجه‬ ‫اة‬ ‫ا‬ ‫ي‬ ‫طر‬ ‫ان‬ ‫ا‬ ‫م‬ ‫ال‬ ‫ا‬ ‫أف‬ ‫اي‬ ‫ا‬ ‫ه‬ ADE ‫اة‬ ‫ا‬ ‫ي‬ ‫طر‬ ‫رن‬ ‫اة‬ ‫ا‬ ‫النتيج‬ ‫ان‬ ‫ا‬ ‫ولك‬ ) Hopscotch ‫ال‬ ‫ا‬ ‫أف‬ ‫اي‬ ‫ا‬ ‫ه‬ ‫اة‬ ‫ي‬ ‫طر‬ ‫من‬ ADI ‫ا‬ ‫ي‬ ‫ن‬ ‫ا‬ ‫خ‬ ‫از‬ ‫رل‬ ‫اا‬ ‫ححت‬ ‫اا‬ ‫ألنه‬ ‫اار‬ ‫األقو‬ ‫اة‬ ‫الاالثي‬ ‫افوفات‬ ‫المص‬ ‫ايمة‬ ‫ص‬ ‫اوي‬ ‫ححت‬ ‫اا‬ ‫أنه‬ ‫از‬ ‫رل‬ ‫اافة‬ ‫اإلض‬ ‫ر‬ Tridiagonal ‫الاالثة.‬ ‫الورق‬ ‫من‬ ‫لكل‬ ‫ارب‬ ‫وح‬ ‫ية‬ ‫ار‬ ‫ر‬ ‫است‬ ‫و‬ ‫وحية‬ ‫ث‬ ‫درسنا‬ ‫ما‬ . ‫المفتاحية:‬ ‫الكلمات‬ ‫گراي‬ ‫أنموذج‬ -‫طريقة‬ , ‫الصريحة‬ ‫المتعاقبة‬ ‫المتجهات‬ ‫طريقة‬ ‫المنتهية,‬ ‫الفروقات‬ ‫طرائق‬ ‫سكوت,‬ ‫ال‬ ‫المتعاقبة‬ ‫المتجهات‬ ‫هبسكوج.‬ ‫طريقة‬ , ‫ضمنية‬

The Burger's-Huxley equation has been solved numerically by using two finite difference methods, the explicit scheme and the Crank-Nicholson scheme. A comparison between the two schemes has been made and it has been found that, the first scheme is simpler while the second scheme is more accurate and has faster convergent. Also, the stability analysis of the two methods by using Fourier (Von Neumann) method has been done and the results were that, the explicit scheme is stable under the condition