Category: Numerical Analysis

If 17a26 is divisible by 7 ,then find the value of a?

f(x)=0

f(x)=X cube -2x-5

X equals to zero, f of Sirohi is less than 0

X equals to 1, f of 1 equals to minus 6 less than zero

X equals to 2, f of two equals to minus 1 less than zero

X equals to 3, you have to equals to plus 6 greater than zero

therefore roots lies between (2,3)

let it’s not equals to 2

f of X equals to x cube minus 2 x-5

f dash of X equals to 3 x square – 2 put a not equals to X when then X1 equals to it’s not minus f of X not by if dash of X not X1 equals to 2 – f of two divided by if dash of 2 X1 = 2 – 1 extra equals to 2.0 94, X3 equals to 2.094 therefore X equals to 2.094

Problem Set

The PDF below contains the specific problems for Project 3.

MATLAB Starter Files

To help you get started, incomplete MATLAB templates are provided. These files contain the structure, comments, and plotting code you must fill in the missing code where indicated by:

   = ;  % <-- COMPLETE: [description]

Each COMPLETE section includes a description of the mathematical formula you need to implement. All figures are saved automatically as .png files in your working directory.

Submission Instructions

Please submit the following two items on Canvas.

1. MATLAB Code (.m files)

Upload the following scripts and functions. Ensure your code is well-commented and runs without errors.

• Reusable Solver Functions:

• • fd_bvp_1d.m (1D BVP finite difference solver)
  • fd_poisson_2d.m (2D Poisson five-point stencil solver)

• Problem Scripts:

• • problem1_convergence.m(Problem 1 Grid refinement convergence study)
  • problem2_peclet.m (Problem 2 Central vs. upwind for convection-diffusion)
  • problem3_poisson.m (Problem 3 2D Poisson visualization and convergence)
  • problem4_iterative.m (Problem 4 Jacobi, Gauss-Seidel, and SOR comparison)

2. Written Report (PDF)

Submit a single PDF file (max 10 pages) containing:

• Figures: All plots generated by your MATLAB code with proper labels, titles, and legends (Blue sections).
• Tables: Convergence tables, iteration count tables, and solution range tables as specified.
• Critical Thinking: Written answers for Problems 1C, 2C, 3C, and 4C (Orange sections). Superficial answers will not receive full credit.

Recommended (not graded): Include a README.md describing each .m file and how to run the scripts. A template is provided in the starter files.

Grading

Problems 14: 25 points each (100 total). Points are distributed roughly equally between correct working code, properly formatted figures, and thoughtful Critical Thinking answers.

will be proud you are wil be successful but you are not bellive own you are not success

The PDF below contains the specific problems for Project 2.

MATLAB Starter Files

To help you get started, incomplete MATLAB templates are provided. These files contain the structure, comments, and plotting code you must fill in the missing code where indicated by:

[t, y] = ; % <-- COMPLETE: call forward_euler_sys

Each TODO section includes hints and the mathematical formula you need to implement. All figures are saved automatically as .png files in your working directory.Submission Instructions

Please submit the following two items on Canvas.

1. MATLAB Code (.m files)

Upload the following scripts and functions. Ensure your code is well-commented and runs without errors.

• Reusable Solver Functions:
  • forward_euler_sys.m (Forward Euler for systems)
  • trapezoidal_sys.m (Trapezoidal Rule for systems)
  • backward_euler_sys.m (Backward Euler with Newton/fixed-point)
  • rk_explicit.m (General explicit Runge-Kutta solver)
  • dopri45.m (Dormand-Prince adaptive RK4(5))
• Problem Scripts:
  • problem1_pendulum.m (Problem 1 Phase portraits and energy drift)
  • problem2_robertson.m (Problem 2 Stiff system, Newton vs fixed-point)
  • problem3_convergence.m (Problem 3 RK convergence study)
  • problem4_adaptive.m (Problem 4 Adaptive vs fixed-step on satellite orbit)
  • problem5_vanderpol.m (Bonus Problem 5 Van der Pol stiffness spectrum)
• Provided (do not modify):
  • fSat.m (Right-hand side for the restricted 3-body problem)

2. Written Report (PDF)

Submit a single PDF file (max 12 pages) containing:

• Figures: All plots generated by your MATLAB code with proper labels, titles, and legends (Blue sections).
• Tables: Summary tables for Problems 2, 3, and 5 as specified.
• Critical Thinking: Written answers for Problems 1C, 2C, 3C, and 4C (Orange sections). Superficial answers will not receive full credit.
• Bonus: If attempting Problem 5, include the method comparison figure, step-size history, scaling plot, and Part B analysis.

Grading

Problems 14: 25 points each (100 total). Bonus Problem 5: up to +15 points. Points earned on Problem 5 can offset deductions on Problems 14, but the project total is capped at 100.

solve tutorials with explanations. Should be clear.

Use Excel to perform all the following analysis in the assigment.