dy/dx - = 1 - y,y(0) = 0 is an example of

[zaasmi]

Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 Using Modified Euler’s method, for the range 0⩽t⩽0.60⩽t⩽0.6, h = 0.1 is

[zaasmi]

If yn+1=yn+16(K1+2K2+2k3+k4)yn+1=yn+16(K1+2K2+2k3+k4) then, K2K2 is:

[zaasmi]

Multistep method does not improves the accuracy of the answer at each step.

[zaasmi]

@zaasmi said in MTH603 Quiz 3 Solution and Discussion:

Multistep method does not improves the accuracy of the answer at each step.

Multistep methods attempt to gain efficiency by keeping and using the information from previous steps rather than discarding it. Consequently, multistep methods refer to several previous points and derivative values.

[zaasmi]

In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

[zaasmi]

@zaasmi said in MTH603 Quiz 3 Solution and Discussion:

In Runge – Kutta Method, we do not need to calculate higher order derivatives and find greater accuracy.

R.K Methods do not require prior calculation of higher derivatives of y(x) ,as the Taylor method does. Since the differential equations using in applications are often complicated, the calculation of derivatives may be difficult

[zaasmi]

Given that dydt=y−ty+tdydt=y−ty+t with the initial condition y=1,t=0y=1,t=0 find the 3rd term in Taylor series when t=0.3 and y//= 0.2.

[zaasmi]

@zaasmi said in MTH603 Quiz 3 Solution and Discussion:

Given that dydt=y−ty+tdydt=y−ty+t with the initial condition y=1,t=0y=1,t=0 find the 3rd term in Taylor series when t=0.3 and y//= 0.2.

Solution

[zaasmi]

Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

[zaasmi]

@zaasmi said in MTH603 Quiz 3 Solution and Discussion:

Given that dydt=t+y√dydt=t+y with the initial condition y0=1att0=0y0=1att0=0 find the 2nd term in Taylor series when t=1, y/ =0.2, and h=0.1.

Solution Web

[zaasmi]

Euler’s Method numerically computes the approximate ________ of a function.

[zaasmi]

@zaasmi said in MTH603 Quiz 3 Solution and Discussion:

Euler’s Method numerically computes the approximate ________ of a function.

Euler’s method is a numerical tool for approximating values for solutions of differential equations.

[cyberian]

the area of a trapeziod is obtained by adding the area of a … and a triangle.

[cyberian]

@cyberian said in MTH603 Quiz 3 Solution and Discussion:

the area of a trapeziod is obtained by adding the area of a … and a triangle.

The area of a trapezoid can be obtained by adding the area of a rectangle and a triangle.

[cyberian]

In double integration, the process involves integrating a function of two variables over a two-dimensional region. The procedure typically follows these steps:

Keep One Variable Fixed: Select one of the variables (say
𝑥
x) to be integrated first while keeping the other variable (
𝑦
y) fixed. This creates an inner integral.

Integrate with Respect to the Fixed Variable: Perform the integration with respect to the selected variable (
𝑥
x), treating the other variable (
𝑦
y) as a constant. This is known as the inner integral.

Integrate the Result with Respect to the Remaining Variable: After integrating with respect to
𝑥
x, integrate the resulting expression with respect to the remaining variable (
𝑦
y). This is known as the outer integral.

[cyberian]

which of the following reason lead towards the numerical integration methods?

Analytical evaluation of integral is very complicated
All above choices are true
Integrand is given in tabular form
Analytical evaluation of integral is impossible