The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is de...The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is developed and used to solve the ordinary differential equation(ODEs)systems based on the finite difference method of lines and the precise integration method(PIM).Two examples of Poisson^equation problems are given:a boundary value problem and an ODE eigenvalue problem.The PIMOL can effectively reduce a semi-discrete ODE problem to a linear algebraic matrix equation.Numerical results show that the PIMOL is a powerful method.展开更多
The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines(PIMOL),which is developed and used to solve the ordinary differential equation(ODE)systems based on the fini...The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines(PIMOL),which is developed and used to solve the ordinary differential equation(ODE)systems based on the finite difference method of lines and the precise integration method.The irregular domain problem is mainly discussed in this paper.Three classical examples of Poisson^equation problems are given,including one regular and two irregular domain examples.The PIMOL reduces a semi-discrete ODE problem to a linear algebraic matrix equation and does not require domain mapping for treating the irregular domain problem.Numerical results show that the PIMOL is a powerful method.展开更多
文摘The aim of this paper is to introduce a new semi-analytical method,namely PIMOL(precise integration method of lines,the parametric finite difference method of lines based on the precise integration method),which is developed and used to solve the ordinary differential equation(ODEs)systems based on the finite difference method of lines and the precise integration method(PIM).Two examples of Poisson^equation problems are given:a boundary value problem and an ODE eigenvalue problem.The PIMOL can effectively reduce a semi-discrete ODE problem to a linear algebraic matrix equation.Numerical results show that the PIMOL is a powerful method.
文摘The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines(PIMOL),which is developed and used to solve the ordinary differential equation(ODE)systems based on the finite difference method of lines and the precise integration method.The irregular domain problem is mainly discussed in this paper.Three classical examples of Poisson^equation problems are given,including one regular and two irregular domain examples.The PIMOL reduces a semi-discrete ODE problem to a linear algebraic matrix equation and does not require domain mapping for treating the irregular domain problem.Numerical results show that the PIMOL is a powerful method.
