This repository contains MATLAB implementations of various numerical methods widely used in scientific computing, geophysics, and engineering. The codes are structured as standalone scripts and functions, designed for easy testing and learning.
| File/Folder | Description |
|---|---|
Cubic_spline_interp.m |
Cubic spline interpolation algorithm |
Quad_spline_interp.m |
Quadratic spline interpolation implementation |
Linearinterp.m |
Linear interpolation function |
Polynomial_interp.m |
Polynomial interpolation |
ErrorsNumInt.m |
Error estimation in numerical integration |
MidPoint_interp.m |
Mid-point integration method |
Num_Integral.m |
Simpson’s Rule and numerical integration methods |
MovingBlock.m |
Moving average / block smoothing |
EigenVec.m |
Eigenvalue and eigenvector calculation |
fourier.m |
Basic Fourier transform implementation |
fourier_approximation.m |
Fourier approximation for signal analysis |
heat1D_explicit.m |
1D heat conduction using finite difference method (explicit) |
linear_inversion.m |
Linear inversion applied to geophysical problems |
newtons_method.m |
Root finding using Newton-Raphson method |
random_seismogram.m |
Fourier approximation of a seismogram signal |
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✅ Numerical Interpolation
Linear, Polynomial, Cubic and Quadratic Spline Interpolation -
✅ Numerical Integration
Midpoint, Trapezoidal, and Simpson's Rule -
✅ Error Estimation
Evaluate numerical accuracy and convergence behavior -
✅ Signal Processing
Fourier transform and approximation, synthetic seismograms -
✅ Heat Transfer Modelling
Explicit finite difference solution for 1D heat conduction -
✅ Geophysical Applications
Basic linear inversion and random seismogram simulation