📘 numerical analysis

1. **Problem Statement:** Find $f(22)$ using the Gauss forward interpolation formula given the data points: $x$: 20, 25, 30, 35, 40, 45

1. **Problem Statement:** Find the first derivative $f'(x)$ and second derivative $f''(x)$ at $x=1$ using the forward difference operator from the given table:

1. **Problem Statement:** We are given values of $y$ at points $x = 20, 25, 30, 35, 40, 45$ and want to find $f(22)$ using the Gauss forward interpolation formula. 2. **Given Data:

1. **Problem Statement:** Find the second derivative $f''(3)$ of the function $f(x) = x^4$ at $x=3$ using the forward difference operator with given data points $x = 0, 3, 6, 9, 12

1. **Énoncé du problème** : On considère l'équation différentielle $$-u''(x) + c(x)u(x) = f(x), \quad x \in [0,1],$$ avec les conditions aux limites $$u(0) = 0$$ et $$u(1) = 0$$, o

1. The user asked if I know the content and topics of the book "Numerical Analysis" by Burden & Faires, 9th Edition. 2. This is a non-math question about book content, not a math p

1. **Problem statement:** Calculate the relative error given an approximate value of 35.88 and an actual value of 36.24. 2. **Formula for relative error:**

1. **State the problem:** We need to find the relative percentage error of $x - y$ when $x$ and $y$ are chopped to five decimal digits. 2. **Given values:**

1. مسئله: یافتن چندجمله‌ای درونیاب به روش تفاضلات تقسیم شده نیوتن برای نقاط داده شده $(-1,-3)$، $(1,0)$ و $(2,4)$ است. 2. فرمول چندجمله‌ای نیوتن:

1. مسئله: با استفاده از چند جمله‌ای‌های لاگرانژ، چند جمله‌ای درونیاب تابع داده شده در نقاط $x_i = 0, 1, 2, 4$ با مقادیر متناظر $f_i = 1, 1, 2, 5$ را بیابید. 2. فرمول چند جمله‌ای لا

1. Masalah yang diberikan adalah persamaan iteratif untuk $u^{n+1}$ yang melibatkan beberapa variabel dan operator linear. 2. Persamaan utama adalah:

1. **Problem:** Describe the basic concepts of errors using $a=\sqrt{2}$ (exact) and $\bar{a}=1.414$ (approximate).\n\n2. **Error Concepts:** The **absolute error** is $|a - \bar{a

1. **Problem Q1 (A): Describe basic concepts of errors using $a=\sqrt{2}$ and $\bar{a}=1.414$.** 2. The exact value is $a=\sqrt{2} \approx 1.414213562$ and the approximate value is

1. **Problem statement:** (A) Considering an exact value of variable $a = \sqrt{2}$ and its approximate $\bar{a} = 1.414$, describe the basic concepts of errors.

1. **Problem Statement:** We are given data points for $x$ and $f(x)$ and asked to find $f(0.58)$ using Newton's interpolation method of order 3. 2. **Newton's Interpolation Formul

1. **Énoncé du problème :** Nous cherchons à estimer les paramètres $a$ et $b$ d'un modèle non linéaire à partir de données expérimentales $(\gamma, y_i)$.

1. **Problem Statement:** Use Newton's forward interpolation formula to calculate the values of $s_n$, $2s_n$, $3s_n$, $4s_n$, $5s_n$, and $k s_n$ for $k=5$ given $s_n = n^3 = \fra

1. **Problem statement:** We have the boundary value problem (BVP) $$u''''(x) = f(x),$$ with boundary conditions $$u(0)=0,$$ $$u'(0)=0,$$ $$u''(1)=0,$$ and $$u'''(1)=0.$$ We want t

1. **Stating the problem:** Define error, source of error, and type of error in numerical analysis. 2. **Definition of Error:** In numerical analysis, an error is the difference be

1. **State the problem:** We want to find the constant $p$ and the error term for the quadrature formula:

1. **Problem Statement:** Understand polynomial interpolation and how it is used in numerical differentiation and integration. 2. **Polynomial Interpolation:** Given a set of point