Numerical convergence and stability analysis for a nonlinear mathematical model of prostate cancer. (English) Zbl 1535.65235
Summary: The main target of this paper is to present an efficient method to solve a nonlinear free boundary mathematical model of prostate tumor. This model consists of two parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a prostate tumor. We start our discussion by using the front fixing method to fix the free domain. Then, after employing a nonclassical finite difference and the collocation methods on this model, their stability and convergence are proved analytically. Finally, some numerical results are considered to show the efficiency of the mentioned methods.
{© 2023 Wiley Periodicals LLC.}
{© 2023 Wiley Periodicals LLC.}
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35K55 | Nonlinear parabolic equations |
| 35R35 | Free boundary problems for PDEs |
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 92C50 | Medical applications (general) |
| 92C37 | Cell biology |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
convergence and stability; finite difference method; free boundary problem; nonlinear parabolic equation; prostate cancer model; spectral methodReferences:
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