ADMATH LAB SA4
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24 Terms
ODE
What is an equation containing derivatives of one or more dependent variables with respect to a single independent variable?
PDE
What is an equation involving partial derivatives with respect to two or more independent variables?
Initial Value Problem
What type of mathematical problem seeks an ODE solution satisfying initial conditions?
Initial conditions
What are subsidiary conditions given at the same value of the independent variable?
Boundary Value Problem
What type of problem seeks an ODE solution satisfying boundary conditions?
Boundary conditions
What are subsidiary conditions given at more than one value of the independent variable?
Step size
What does the variable 'h' represent in numerical ODE solutions?
Euler's Method
What is the simplest first-order Runge-Kutta numerical method?
Runge-Kutta Method
Which numerical class obtains high accuracy without needing higher derivatives?
Heun's Method
Which RK2 method uses the constant a2 = 0.5?
Midpoint Method
Which RK2 method uses the constant a2 = 1?
Ralston's Method
Which RK2 method uses the constant a2 = 2/3?
RK4
What is the most popular and widely used Runge-Kutta method?
Finite Difference Method
Which BVP solution method uses algebraic approximations for derivatives?
Forward Difference
Which FDM approximation uses the current and next points (i and i+1)?
Backward Difference
Which FDM approximation uses the current and previous points (i and i-1)?
Central Difference
Which FDM approximation for y' uses points i+1 and i-1?
Shooting Method
Which method converts a boundary value problem into an equivalent initial value problem?
Trial-and-error
What general approach is implemented when using the Shooting Method?
Guess
In the Shooting Method, what type of value is used for the second initial condition?
Linear interpolation
What formula is used to determine the third guess in the Shooting Method?
n
Which variable typically represents the number of sub-intervals?
Order of ODE
The required number of boundary conditions is equal to what property of the ODE?
Interval
In BVP solutions, what is the range between the lower and upper limits of x?