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# Numerical Analysis

### Mixture Problem as a Differential Equation.

Please solve using separation of variables method. A certain chemical is converted into another chemical by a chemical reaction. The rate at which the first chemical is converted is proportional to the amount of this chemical present at any instant. Ten percent of the original amount of the first chemical has been convert

### Numerical Analysis - Fixed Point iteration method.

Fixed Point iteration method. Use a fixed-point iteration method to find an approximation to that is accurate within 10-4 See attached file for full problem description.

### Solving Bernoulli Equations

X*(dy/dx) + y = -2*x^6*y^4

### Breaking an Eigenvalue Equation into Domains

Examine the eigenvalue equation below and then break the domain into four different regions (like a>0) and b=0 is one such domain. Describe the behavior of the equation in each domain.... Please see the attached file for the fully formatted problems. keywords: differential equations, trace, node

### Working with half life of a radioactive material

Polonium-210 has a half life of 140 days If a sample has a mass of 200 mg find a function describing the mass that remains after t days When will the mass be reduced to 10 mg?

Adam collects stamps. He has 18 bird stamps,9 flower stamps and 12 butterfly stamps. For a school project, he will display an equal number of each kind of stamp on a small poster boards. What is the greatest number of poster boards Adam can make if he uses all of the stamps?

### Numerical Analysis Problem/Secan Method

(See attached file for full problem description with proper symbols) --- A) Consider a variation of Newton's method in which only one derivative is needed; that is . Find C and s such that . B) Find the conditions on to ensure that the iteration will converge linearly ( ) to a zero of f if started near the zero.

### Numerical Stability

(See attached file for full problem description with equations) --- There is a function f of the form for which and . Determine and , and assess the sensitivity of these parameters to slight changes in the values of f at the two indicated points. ---

### Solving an IVP with Maple: Euler and Improved Euler Method

Use Maple to solve this exercise: Consider the following (IVP) logistic model p' = 10p(1-p) with p(0)=0.1 1. Solve this IVP and graph the solution over the interval [0, 10], Write down the Euler approximation, and Improved Euler approximation with step size h. 2. Compute and plot the first 100 points of the Euler method

### Solving 2 ODE's with One Unknown

Given that: dMN/dt = P¬oert - pMN + m(MS - MN) dMS/dt = m(MN - MS) - pMS¬ MN¬ (0) = MS (0) = 0 And using: M¬N + MS = [Po/(r + p)](ert - e-pt) Show that MS(t) = And show that R = MN(t) / MS(t) = Please see the attached file for the fully formatted problems.

### PDE : Riemann's Method for Solving Cauchy Problem

Hello. Thanks for help! I will use * to indicate a partial derivative. For example, u*x denotes the partial derivative of u with respect to x. This is the probelm: Use Riemann's method to solve the Cauchy problem: u*xx + 4u*xy +3u*yy = 1, u=1 and u*n = square root of 5 times x, on the intial curve y=2x. If this

### Wave Equation : Solve a PDE

Please see the attached file for the fully formatted problems.

### Numerical Methods, 400 Undergraduate level.

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. If there is anything unclear in the question, let me know. Thank you. (Complete problem in attachment)

### Numerical Methods: Fixed-Point Iteration

Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. Let g(x) = 0.5x + 1.5 and p0 = 4, and consider fixed-point iteration. a) Show that the fixed point is P=3 b) Show that |P - Pn| = |P - Pn-1|/2 for n = 1, 2, 3... c) Show that |P - Pn| = |P - P0|/2^2 for n = 1, 2, 3...

### Three=digit rounding arithmetic

The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. 7. Use three-digit rounding arithmetic to compute the following sums... Please see attached.

### Existence and uniqueness theorem

I am looking for the solution of this problem. It involves a little bit of theory in the second part. In the solution give a detailed solution showing all assumptions and theorems.

### Partial Differential for Diffusion Equation

Suppose that u(x,t) satisfies the diffusion equation... for 0<x<L and t>0, and the Robin boundary conditions... where k, L, a0 and aL are all positive constants. Show that... is a decreasing function of t. Please see attached for full question.

### Solving the Initial Value Problem

Please solve the initial value problem. See attached file.

### Numerical Methods - Spline

Consider the natural cubic spline function s(x) interpolation the following data... Please see attached for full question.

### Heat Equation, Boundary & Steady State Conditions, Initial Value

Please help with the following problems involving numerical analysis. (a) Find all the separated solutions of the attached heat equation (satisfying the attached boundary condition) (b) Use these separated solutions to write a series solution for the initial value problem posed by the attached pde and the attached boundar

### ELEMENTARY NUMERICAL ANALYSIS by ATKINSON HAN

Please see the attached file for full problem description.

### Using Malthus Method

Suppose that a culture of bacteria has initial population of n=100. If the population doubles every three days, determine the number of bacteria present after 30 days. How much time is required for the population to reach 4250 in number

### Dipoles, Quadrupoles and Laplacian: Limiting Potential

Consider a dipole of strength D, oriented along the x-axis and located at the point x =E/2 , y = 0, z = 0, and a dipole of strength -D, oriented along the x-axis at the point x = - , y = 0, z = 0. Write the expression for the potential for these two dipoles. Take the limit as , and show that the limiting potential is given by

### Solve Helmholtz Equation : Bessel's Equations

A)Solve the Helmholtz equation when u is a function of r only in 2-D. b)Solve the Helmholtz equation when u is a function of r only in 3-D. (see attachment for full question)

### Rectangular Drum Problem #9

Just #9, please. Solve the rectangular drum problem u_xx + u_yy = (c^-2)u_tt 0 < x < a 0 < y < b t > 0 u(x,y,t) = 0, u(a,y,t) = 0 0 < y < b t > 0 u(x,0,t) = 0, u(x,b,t) = 0 0 < x < a t> 0 u(x,y,0) = xy and (u_t)(x,y,0) = 0. Find the solution explicitly in the case

### ODEs: Sturm-Liouville Form; Weight Function; Inner Product

Write each of these ODEs in Sturm-Liouville form, and identify the weight function that would be used in defining an appropriate inner product {see attachment for ODEs} Use words to describe the solution process. Use appropriate math symbol editor like LateX. Please no stuff like <=.

### Initial Value Problem (IVP); Euler's Method; Step Sizes

4. Consider the initial value problem (IVP): y'(t) = 3+t+y y(0)=1 a) Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)? b) Use the computer (e.g. ODE Architect, ODE Toolkit, or your own program) to approximate y(1) using step sizes of 0.1, 0.05,

### Numerical Euler's Method for Initial Value Problem

Consider the initial value problem (IVP): y'(t) = y^2 y(0)=1 Approximate y(1) using Euler's method and step sizes of 0.25. Perform these calculations by hand (using a calculator for arithmetic is ok). What is the true value of y(1)?

### Solve: A Second Order ODE

Please solve for the following: Find a particular solution to y'' + 5y' +4y = -13te^(3t) Show all work.

### Solve a 2nd order ODE.

Find particular solution to y'' - 8y' +16y = 19.5e^(4t)