Solving 2D Wave Equation Using Finite Difference Method
Implement numerical solution for 2D wave equation with Finite Difference Method, including grid discretization, derivative approximation, and time-stepping algorithm
Finite Difference Method: A Numerical Approach for Solving Differential and Integro-Differential Equations
The Finite Difference Method (FDM) is a numerical technique for approximating solutions to differential equations and integro-differential equations. The core concept involves discretizing a continuous domain into a grid of finite discrete points (nodes), where continuous functions are approximated by discrete grid functions. Derivatives in the original equations and boundary conditions are replaced by difference quotients, while integrals are approximated by discrete sums, transforming the system into an algebraic finite difference equations system. Solving this system yields approximate solutions at discrete points, which can then be interpolated to obtain solutions over the entire domain. Implementation typically involves grid generation, difference operator construction, and linear system solvers.
Solving Partial Differential Equations Using Finite Difference Method
Implementing finite difference method for PDEs with Gauss-Seidel iteration, utilizing the infinity norm of the matrix difference between consecutive iterations as convergence criterion.
Numerical Simulation of Elastic Wave Equations Using Finite Difference Method
MATLAB implementation of finite difference method for numerical simulation of elastic wave equations with code structure and algorithm explanations
Development of a Reynolds Equation Solver Using Finite Difference Method in MATLAB
Implementation of a Reynolds equation solution approach utilizing finite difference method with MATLAB, including numerical discretization and computational algorithm design.
One-Dimensional Wave Equation Computation
A program for computing the one-dimensional wave equation using the finite difference method, featuring numerical implementation details and practical applications
Solving Poisson's Equation Using Finite Difference Method
Finite Difference Method for Solving Poisson's Equation - An Example Comparing Analytical and Numerical Solutions with Code Implementation
Solving the Reynolds Equation Using the Finite Difference Method
Implementation of the Reynolds equation solution via finite difference method with a concise MATLAB program, including parameter explanations and numerical approaches
Finite Difference Method (FDM) for Field Discretization and Numerical Solution
The Finite Difference Method (FDM) discretizes a computational domain into small grid elements, applying difference principles to transform the problem of solving continuous Poisson equations into solving systems of difference equations at grid nodes.
Finite Difference Method for Solving Two-Dimensional Electric Fields
Solving two-dimensional electric fields using the finite difference method, covering implementations with square, rectangular, and regular hexagonal grid discretizations, alongside two-dimensional infinite domain problems