Consider the Problem Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$

question 29

Multiple Choice

Consider the problem $c \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( 0 , t ) = 0 , u ( 1 , t ) = 2 , u ( x , 0 ) = 2 x ^ { 2 }$ . Replace $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } }$ with a central difference approximation with $h = 1 / 3$ and $\frac { \partial u } { \partial t }$ with a forward difference approximation with $k = 1 / 2$ . The resulting equation is

• A) \(c [ u ( x + h , t ) + 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k\)
• B) \(c [ u ( x + h , t ) + 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) + u ( x , t ) ) / k\)
• C) \(c [ u ( x + h , t ) - 2 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k\)
• D) \(c [ u ( x + h , t ) - 4 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) + u ( x , t ) ) / k\)
• E) \(c [ u ( x + h , t ) - 4 u ( x , t ) + u ( x - h , t ) ] / h ^ { 2 } = ( u ( x , t + k ) - u ( x , t ) ) / k\)

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Stock Split

A corporate action where a company divides its existing shares into multiple shares to boost the liquidity of the shares, although the overall market capitalization remains unchanged.

Call Option

An economic agreement that grants the buyer the option to acquire an asset such as a stock, bond, commodity, or similar at an agreed-upon price before a certain deadline, without being compelled to do so.

Exercise Price

The price at which an option holder can buy or sell the underlying asset.

Money Spread

The difference between two prices or rates, often used to describe the gap between bid and ask prices in financial markets.