This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev polynomials (MCPs). This method was relying on derivative of MCPs which explicit in the series expansion. The advantage of this method is solved HBVPs without transforming it to a system of lower-order ordinary differential equations (ODEs). This method supported by examples of HBVPs in wide application. The mentioned examples showed that the proposed method is efficient and accurate.
翻译:本文的重点是采用新方法解决线性和非线性较高边界值问题。这种基于光谱法的直接数字方法。这种方法的试算功能是Monic Chebyshev 多元分子(MCPs),这种方法依赖于在序列扩展中明确的MCP的衍生物。这种方法的优点在于解决HBVPs,而没有将其转换为低级普通差分方程(ODEs)系统。这种方法得到广泛应用的HBVPs的例子的支持。所述的例子表明,拟议的方法既有效又准确。