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1. Newton's method
The formula for Newton's method is:
x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}
Where:
- x_{n+1} is the next approximation
- x_n is the current approximation
- f(x) is the function for which we are finding the root
- f'(x) is the derivative of the function
2. Euler's method
The formula for Euler's method is:
y_{n+1} = y_n + hf(t_n, y_n)
Where:
- y_{n+1} is the next approximation of the solution
- y_n is the current approximation of the solution
- h is the step size
- f(t_n, y_n) is the derivative function at (t_n, y_n)
3. Runge-Kutta method
The formula for Runge-Kutta method is:
y_{n+1} = y_n + \frac{h}{6}(k1 + 2k2 + 2k3 + k4)
Where:
- y_{n+1} is the next approximation of the solution
- y_n is the current approximation of the solution
- h is the step size
- k1, k2, k3, k4 are approximations of the derivative function at different points
4. Taylor series
The formula for Taylor series expansion is:
f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + ...
Where:
- f(x) is the function being expanded
- a is the point around which the expansion is being done
5. Lagrange interpolation
The formula for Lagrange interpolation is:
P(x) = \sum_{i=0}^{n} y_i l_i(x)
Where:
- P(x) is the interpolated polynomial
- y_i are the known function values
- l_i(x) are the Lagrange basis polynomials.
Numerical analysis formula calculator is a comprehensive tool for numerical analysis, providing formulas and methods such as Newton's method, Euler's method, Runge-Kutta methods, finite difference method, Taylor series, Lagrange interpolation, and many more.
It covers a wide range of topics including differential equations, integration, matrix operations, eigenvalues, iterative methods, error analysis, and stability analysis.
With over 100 formulas and methods available, numerical analysis formula calculator is a valuable resource for students and professionals in the field of mathematics and engineering.
1. Newton's method
2. Euler's method
3. Runge-Kutta methods
4. Finite difference method
5. Taylor series
6. Lagrange interpolation
7. Neville's algorithm
8. Bisection method
9. Secant method
10. False position method
11. Gauss elimination
12. LU decomposition
13. Cholesky decomposition
14. Gauss-Seidel method
15. Jacobi method
16. Monte Carlo method
17. Simpson's rule
18. Trapezoidal rule
19. Romberg integration
20. Gaussian quadrature
21. Richardson extrapolation
22. Simpson's 3/8 rule
23. Leapfrog method
24. Euler-Cromer method
25. Adams-Bashforth method
26. Adams-Moulton method
27. Heun's method
28. Richardson extrapolation
29. Multistep methods
30. Predictor-corrector methods
31. Finite element method
32. Fourier series
33. Fourier transform
34. Laplace transform
35. Discrete Fourier transform
36. Fast Fourier transform
37. Finite volume method
38. Crank-Nicolson method
39. Spectral methods
40. Richardson extrapolation
41. Chebyshev polynomials
42. Legendre polynomials
43. Finite element analysis
44. Ritz-Galerkin method
45. Stiffness matrix
46. Consistency condition
47. Stability condition
48. Convergence criterion
49. L2 norm
50. Residual error
51. Richardson error
52. Accuracy order
53. Stability region
54. Truncation error
55. Round-off error
56. Taylor expansion
57. Machine epsilon
58. Condition number
59. Vector norms
60. Matrix norms
61. Matrix factorization
62. Eigenvalues
63. Eigenvectors
64. Singular value decomposition
65. QR decomposition
66. Schur decomposition
67. Condition number
68. Variation of parameters
69. Separation of variables
70. Frobenius method
71. Wronskian
72. Homogeneous equation
73. Inhomogeneous equation
74. Green's function
75. Perturbation theory
76. Galerkin method
77. Discrete differentiation
78. Local error
79. Global error
80. Iterative methods
81. Jacobi method
82. Gauss-Seidel method
83. SOR method
84. Preconditioning
85. GMRES method
86. Minimum residual method
87. Biconjugate gradient method
88. Conjugate gradient method
89. Krylov subspace
90. GMRES method
91. Arnoldi iteration
92. Lanczos iteration
93. Error analysis
94. Stability analysis
95. Stiffness analysis
96. Boundary value problem
97. Initial value problem
98. Stability boundary
99. Hyperbolic differential equation
100. Parabolic differential equation
