یک جواب عددی پایدار برای یک مسئله ی کران متحرک معکوس انتقال حرارت با استفاده از روش مارچینگ

نوع مقاله : اصیل

نویسندگان

1 دانشکده ریاضی و علوم کامپیوتر، دانشگاه دامغان

2 گروه ریاضی، دانشگاه شهید چمران اهواز

چکیده

در این مقاله کاربرد روش مارچینگ و روش مولیفیکیشن برای حل یک مسئله کران متحرک مربوط به معادله گرما مورد بررسی قرار میگیرد. دادههای این مسئله بهصورت همراه با اختلال در نظر گرفته میشوند. یک روند منظمسازی براساس روش مولیفیکیشن و نیز روش مارچینگ برای حل مسئله مورد نظر ارائه میگردد و همگرایی و پایداری جواب این روش اثبات می شود. چند مثال عددی به منظور نشان دادن توانایی روش و نیز کارایی آن مورد بررسی قرار میگیرد.

کلیدواژه‌ها


عنوان مقاله [English]

A Stable Numerical Solution of an Inverse Moving Boundary Problem of Heat Conduction Using Discrete Mollification Approach

نویسندگان [English]

  • Morteza Garshasbi 1
  • Hatef Dastour 1
  • Mehdi Jalalvand 2
1 School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
2 Department of Mathematics, Shahid Chamran University, Ahvaz, Iran
چکیده [English]

In this paper the application of marching scheme and mollification approach to solve a one dimensional inverse moving boundary problem for the heat equation is investigated. The problem is considered with noisy data. A regularization method based on marching scheme and discrete mollification approach is developed to solve the proposed problem and the stability and convergence of  numerical solution  is  proved.  To  show  the ability and efficiency of the proposed method,  some numerical experiments are investigated. 

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