Numerical Partial Differential Equations & coding
Paper details:
source book attached. c) Numerical solution. In Section 10 you can find example how to solve PDEs numerically. Transport eq (5.7), parabolic equation (5.12), and wave equation (5.14).. For example, in 10.2 you find info how to solve linear transport equation.
Try to test the different schemes mentioned by making a code. Compute numerical solution. Try to understand criteria for stability of the scheme.
In Section 10.3 there is a similar study of heat equation. Explore both explicit and implicit scheme (10.28) and (10.31). d) Extend the code for 1D in c) to 2D. e)
Study in detail the model described in Section 13. Make codes and solve 1D and 2D model and try to reproduce results shown there. The Reaction-Diffusion System: Pattern formation based on the reaction-diffusion mechanism occurs commonly in geophysical and geological processes.
This needs working code to simulate and create graphs. Style doesn’t matter,
2. Apple Inc.
Section 1 (1.5 pages with double-spaced)
- A brief discussion of the firm’s current short-term objectives and action plans. Again, don’t be vague; provide a few concrete examples.
- A brief discussion of the firm’s functional tactics. Again, don’t be vague; provide a few concrete examples of the functional tactics the firm is using to achieve its short-term objectives and gain a sustainable competitive advantage.
- A brief discussion of the policies the firm uses to aid strategy execution (i.e., policies that empower action). Provide a few noteworthy examples.
- A brief description of the types of executive bonus compensation plans the firm is currently using.
Section 3 (at least 2.5 pages)
- Analyze the firm’s current short-term objectives and action plans. Do they effectively help guide the implementation of the firm’s strategy? In other words, do they effectively facilitate the achievement of the firm’s long-term objectives? Do they possess the qualities of short-term objectives? Do they possess the qualities of objectives?
- Analyze the firm’s functional tactics. That is, analyze the functional tactics the firm is currently using to achieve its short-term objectives and build sustainable competitive advantage. How effective are they? Explain and defend your answer.
- Analyze the policies the firm uses to aid strategy execution (i.e., policies that empower action). Are they appropriate? Why or why not?
- Analyze the appropriateness and effectiveness of the firm’s executive bonus compensation plans. The analysis should focus on the types of problems that can arise because of agency relationships and the “fit” between the firm’s executive compensation plans and its strategic goals.
Section 4 (at least 2 pages)
- Recommend specific short-term objectives and action plans. That is, identify the short-term objectives the firm must achieve to realize the long-term objectives your team has established. Stated differently, identify whatthe firm must accomplish to achieve (or move closer to achieving) its long-term objectives. Specifically, identify at least one short-term objective for each long-term objective your team has established. Remember to make sure your team’s short-term objectives possess the characteristics of effective short-term objectives as well as the basic qualities of objectives. Additionally, each short-term objective must be accompanied by an action plan. As stated in the textbook: “Short-term objectives are usually accompanied by action plans, which enhance these objectives [i.e., short-term objectives] in three ways.” Simply stated, for each short-term objective your team establishes, your team must outline an action plan that identifies:
(1) The functional tactics and activities associated with achieving the short-term objective (i.e., the actions that will be undertaken in each functional area in the near future as part of the business’s effort to achieve the stated short-term objective).
(2) A clear time frame for completing each action (i.e., identify when each action will begin and when each action will be completed).
(3) Identify who is responsible for each action in the plan (e.g., Director of Marketing, Director of Human Resources, etc.).
Note: I strongly recommend summarizing your team’s long-term objectives and grand strategies and associated short-term objectives and action plans in a table of some type (e.g., develop a time-line).
- Recommend policies to aid strategy execution (i.e., policies that empower action).
- Recommend appropriate executive bonus compensation practices. At minimum, propose an appropriate executive bonus compensation plan. Don’t be afraid to put forward an innovative (or novel) plan. Try to design a plan that reduces agency problems (i.e., identify some creative ways in which to minimize agency problems).
Additional section (1 page)
- In other words, recommend specific strategic and operational controls. For example, identify the key assumptions (i.e., premises) the proposed strategy is based on; that is, identify what premises should be monitored. Bottom line, your team should demonstrate that it understands the four basic types of strategic controls outlined in Chapter 13.
The four basic types of strategic controls:
- Premise control: the systematic recognition and analysis of assumptions upon which a strategic plan is based, to determine if those assumptions remain valid in changing circumstances and in light of new information
- Strategic Surveillance: management efforts to monitor a broad range of events inside and more often outside the firm that are likely to affect the course of its strategy over time.
- Special Alert Control: management actions undertaken to thoroughly, and often very rapidly, reconsider a firm’s strategy because of a sudden, unexpected event.
- Implementation control: Management efforts designed to assess whether the overall strategy should be change in light of results associated with the incremental actions that implement the overall strategy. These are usually associated with specific strategic thrusts or projects and with predetermined milestone reviews.
- Recommend actions the organization should take to make the firm more innovative and entrepreneurial and, hence, more competitive.
