In the Previous Problem, Using the Notation $u _ { i j } = u ( x , \mathrm { t } )$

question 34

Multiple Choice

In the previous problem, using the notation $u _ { i j } = u ( x , \mathrm { t } )$ , and letting $\lambda = c k / h$ , the equation becomes

• A) \(u _ { i , j - 1 } = \lambda ^ { 2 } u _ { i + 1 , j } + 2 \left( 1 + \lambda ^ { 2 } \right) u _ { i j } + \lambda ^ { 2 } u _ { i - 1 , j } + u _ { i , j - 1 }\)
• B) \(u _ { i , j - 1 } = \lambda u _ { i + 1 , j } + 2 ( 1 - \lambda ) u _ { i j } + \lambda u _ { i - 1 , j } + u _ { i , j - 1 }\)
• C) \(u _ { i , j + 1 } = \lambda ^ { 2 } u _ { i + 1 , j } + 2 \left( 1 + \lambda ^ { 2 } \right) u _ { i j } + \lambda ^ { 2 } u _ { i - 1 , j } - u _ { i , j - 1 }\)
• D) \(u _ { i , j + 1 } = \lambda ^ { 2 } u _ { i + 1 , j } + 2 \left( 1 - \lambda ^ { 2 } \right) u _ { i j } + \lambda ^ { 2 } u _ { i - 1 , j } - u _ { i , j - 1 }\)
• E) \(u _ { i , j + 1 } = \lambda u _ { i + 1 , j } + ( 1 - \lambda ) u _ { i j } + \lambda u _ { i - 1 , j } - u _ { i , j - 1 }\)

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Definitions:

Budget Constraint

The maximum range of goods and services a consumer is able to purchase, determined by their income and the cost of these goods and services.

Income

The money received by individuals or entities, typically in the form of wages, salaries, or various types of investments returns.

Opportunity Cost

The forfeiture of possible benefits from other options when a specific choice is made.

Real Cost

The total cost of producing a good or service, considering all resources including time and opportunity costs.