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.

]]>]]>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.

]]>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.

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

]]>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.

]]>Euler’s method is only useful for a few steps and small step sizes; however Euler’s method together with Richardson extrapolation may be used to increase the ____________.

Order accuracy is the percentage of all ecommerce orders that are fulfilled and shipped to their final destination without error, such as a mis-pick of an item or incorrect unit quantity. Order accuracy is an important metric to track because it highly impacts customer satisfaction.

]]>Generally, Adams methods are superior of output at many points is needed.

The Adams methods are useful to reduce the number of function calls, but they usually require more CPU time than the Runge-Kutta methods.

]]>**True**

False

As presented here, the method can be used only to find the eigenvalue of A that is largest in absolute value—this eigenvalue is called the dominant … The eigenvectors corresponding to are called dominant eigenvectors of A. 1 i. 2, . . . , n.

]]>**True**

False

**Numerical method.** In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.

True

**False**

If an eigenvalue l of A is known, the corresponding eigenvector(s) may be obtained by … l of a matrix A is the maximum number of linearly independent eigen vectors x of A … If v1, v2, …, vn are the eigenvectors associated with the respective … the eigenvalues of A and then if some of them are multiple, to check if there exist …

]]>True

**False**

If A and B are positive definite, is A + B positive definite? We don’t know … to A. If two matrices have the same n distinct eigenvalues, they’ll be similar to the **same diagonal**

**True**

False

Method of Differences. The method of finite differences gives us a way to calculate a polynomial using its values at several consecutive points. This is often a good approach to finding the general term in a pattern, if we suspect that it follows a polynomial form.

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