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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

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

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