تويت
الطرق العددية للمهندسين Numerical Methods هي فرع من فروع الرياضيات التطبيقية التي تستخدم التقنيات العددية لحل المشكلات في الهندسة. تُستخدم هذه الطرق لتقريب الحلول للمشكلات الهندسية المعقدة ، مثل تلك التي تتضمن معادلات تفاضلية ، والتي لا يمكن حلها تحليليًا. تتضمن الطرق العددية الشائعة المستخدمة في الهندسة طرق الفروق المحدودة وطرق العناصر المحدودة وطرق العناصر الحدودية. تُستخدم هذه الأساليب في مجموعة واسعة من التخصصات الهندسية ، بما في ذلك الهندسة الميكانيكية والكهربائية والمدنية
Numerical methods are techniques by which mathematical problems are formulated so that they can be solved with arithmetic operations. Although there are many kinds of numerical methods, they have one common characteristic: they invariably involve large numbers of tedious arithmetic calculations. It is little wonder that with the development of fast, efficient digital computers, the role of numerical methods in engineering problem solving has increased dramatically in recent years
Since the late 1940s the widespread availability of digital computers has led to a veri-table explosion in the use and development of numerical methods. At first, this growth was somewhat limited by the cost of access to large mainframe computers, and, conse-quently, many engineers continued to use simple analytical approaches in a significant portion of their work. Needless to say, the recent evolution of inexpensive personal computers has given us ready access to powerful computational capabilities. There are several additional reasons why you should study numerical methods:
1. Numerical methods are extremely powerful problem-solving tools. They are capable of handling large systems of equations, nonlinearities, and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically. As such, they greatly enhance your problem-solving skills.
2. During your careers, you may often have occasion to use commercially available prepackaged, or “canned,” computer programs that involve numerical methods. The intelligent use of these programs is often predicated on knowledge of the basic theory underlying the methods.
3. Many problems cannot be approached using canned programs. If you are conversant with numerical methods and are adept at computer programming, you can design your own programs to solve problems without having to buy or commission expensive software.
4. Numerical methods are an efficient vehicle for learning to use computers. It is well known that an effective way to learn programming is to actually write computer programs. Because numerical methods are for the most part designed for implementation on computers, they are ideal for this purpose. Further, they are especially well-suited to illustrate the power and the limitations of computers. When you successfully implement numerical methods on a computer and then apply them to solve otherwise intractable problems, you will be provided with a dramatic demonstration of how computers can serve your professional development. At the same time, you will also learn to acknowledge and control the errors of approximation that are part and parcel of large-scale numerical calculations.
5. Numerical methods provide a vehicle for you to reinforce your understanding of mathematics. Because one function of numerical methods is to reduce higher mathematics to basic arithmetic operations, they get at the “nuts and bolts” of some otherwise obscure topics. Enhanced understanding and insight can result from this alternative perspective
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