Consider the Problem a Finite Difference Approximation of the Solution Is Desired

question 14

Multiple Choice

Consider the problem $\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial y ^ { 2 } } = 0 , u ( 0 , y ) = 0 , u ( x , 0 ) = 0 , u ( 1 , y ) = \sin ( \pi y ) , u ( x , 1 ) = \sin ( \pi x )$ . A finite difference approximation of the solution is desired, using the approximation of the previous problem. Use a mesh size of $h = 1 / 3$ The conditions satisfied by the mesh points on the boundary are Select all that apply.

• A) \(u = 1 / 2 \text { at } ( 1,2 / 3 ) \text { and } ( 2 / 3,1 )\)
• B) \(u = \sqrt { 3 } / 2 \text { at } ( 1,1 / 3 ) \text { and } ( 1 / 3,1 )\)
• C) \(u = 0 \text { at } ( 0,1 / 3 ) \text { and } ( 1 / 3,0 )\)
• D) \(u = 0 \text { at } ( 0,2 / 3 ) \text { and } ( 2 / 3,0 )\)
• E) \(u = 0 \text { at } ( 1 / 3,1 / 3 ) \text { and } ( 2 / 3,2 / 3 )\)

---

Definitions:

Acetylcholine

is a neurotransmitter in the nervous system that plays an essential role in muscle contraction and aids in arousal, attention, memory, and motivation.

Genetic Component

Refers to the part of an individual's traits or conditions that are determined by genes, encompassing aspects like inherited characteristics, susceptibility to diseases, and physical attributes.

Serotonin

A neurotransmitter that plays a key role in mood regulation, digestion, sleep, and other bodily functions.

Genetic Components

The elements of an organism's genetic makeup that determine inherited characteristics and predispositions.