Difference Equations/معادلات الفرق
The study covers a range of fundamental topics in difference equations and their mathematical applications. It begins with an introduction to linear difference equations with constant coefficients, addressing both homogeneous and non-homogeneous equations with illustrative examples. then explores th...
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| Format: | Livre |
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INP
2024
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| Accès en ligne: | http://repository.inp.edu.eg//handle/123456789/5679 |
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| _version_ | 1853147120904699904 |
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| author | I. Abdel Karim, Abbas |
| author_facet | I. Abdel Karim, Abbas |
| author_sort | I. Abdel Karim, Abbas |
| collection | DSpace |
| description | The study covers a range of fundamental topics in difference equations and their mathematical applications. It begins with an introduction to linear difference equations with constant coefficients, addressing both homogeneous and non-homogeneous equations with illustrative examples. then explores the use of difference equations in calculating Fibonacci numbers and their algorithmic applications, as well as their use in integrations and the calculation of special functions, such as Chebyshev polynomials and Legendre polynomials. The stability of numerical methods for solving differential equations, including the Euler-Cauchy method and Simpson’s rule, is also discussed. It includes flowcharts for various algorithms and tests for evaluating these methods. |
| format | Book |
| id | oai:repository.inp.ed.eg:123456789-5679 |
| institution | My University |
| publishDate | 2024 |
| publisher | INP |
| record_format | dspace |
| spelling | oai:repository.inp.ed.eg:123456789-56792025-01-16T11:51:06Z Difference Equations/معادلات الفرق I. Abdel Karim, Abbas The study covers a range of fundamental topics in difference equations and their mathematical applications. It begins with an introduction to linear difference equations with constant coefficients, addressing both homogeneous and non-homogeneous equations with illustrative examples. then explores the use of difference equations in calculating Fibonacci numbers and their algorithmic applications, as well as their use in integrations and the calculation of special functions, such as Chebyshev polynomials and Legendre polynomials. The stability of numerical methods for solving differential equations, including the Euler-Cauchy method and Simpson’s rule, is also discussed. It includes flowcharts for various algorithms and tests for evaluating these methods. تتناول الدراسة مجموعة من المواضيع الأساسية في المعادلات الفرقية واستخداماتها الرياضية. يبدأ بمقدمة عن المعادلات الفرقية الخطية مع معاملات ثابتة، حيث يتم تناول المعادلات المتجانسة وغير المتجانسة مع أمثلة توضيحية. ثم تناقش استخدام المعادلات الفرقية في حساب أرقام فيبوناتشي وتطبيقاتها في الخوارزميات، بالإضافة إلى مناقشة كيفية استخدام المعادلات الفرقية في التكاملات الرياضية وحساب الدوال الخاصة مثل متعددات تسيبيشيف ومتعددات ليجوندر. تتناول المذكرة أيضًا استقرار الطرق العددية لحل المعادلات التفاضلية باستخدام طرق مثل طريقة أويلر-كاوشي وطريقة سيمبسون. وفي الختام، توفر العديد من الرسوم البيانية والخوارزميات لاختبار وتحليل هذه الطرق. 2024-12-24T08:05:30Z 2024-12-24T08:05:30Z 1964-11 Book http://repository.inp.edu.eg//handle/123456789/5679 سلسلة مذكرات خارجية رقم (507); application/pdf INP |
| spellingShingle | I. Abdel Karim, Abbas Difference Equations/معادلات الفرق |
| title | Difference Equations/معادلات الفرق |
| title_full | Difference Equations/معادلات الفرق |
| title_fullStr | Difference Equations/معادلات الفرق |
| title_full_unstemmed | Difference Equations/معادلات الفرق |
| title_short | Difference Equations/معادلات الفرق |
| title_sort | difference equations معادلات الفرق |
| url | http://repository.inp.edu.eg//handle/123456789/5679 |
| work_keys_str_mv | AT iabdelkarimabbas differenceequationsmʿạdlạtạlfrq |