Semi-Analytical Solution of the 1D Helmholtz Equation, Obtained from Inversion of Symmetric Tridiagonal Matrix

A Semi-Analytical Method for the Solution of Helmholtz Equation

This note is concerned with a semi-analytical method for the solution of 2-D Helmholtz equation in unit square. The method uses orthogonal functions to project the problem down to finite dimensional space. After the projection, the problem simplifies to that of obtaining solutions for second order constant coefficient differential equations which can be done analytically. Numerical results indi...

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...

Instantaneous Bethe–salpeter Equation: (semi-)analytical Solution

The Bethe–Salpeter equation for bound states of a fermion–antifermion pair in the instantaneous approximation for the involved interaction kernel is converted into an equivalent matrix eigenvalue problem with explicitly (algebraically) given matrices. PACS numbers : 11.10.St, 03.65.Ge ∗ E-mail address : [email protected] ‡ E-mail address : [email protected] † E-mail address : franz.schoebe...

Cubic spline Numerov type approach for solution of Helmholtz equation

We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

Iterative Method for Mirror-Symmetric Solution of Matrix Equation AXB + CY D = E