The present article deals with the study of generalized curvature equality and inequality. We first derive equality involving mean curvature vector and second fundamental form for sequential warped product submanifolds of a nearly Kähler manifold and then present Lawson-Simons type inequality (Lawson and Simons, Ann. of Math. 98:427–450, 1973) in generalized complex space form that extends the result derived by Sahin in Sahin (Period Math. Hung., 2021). Meanwhile, some special cases and a numerical example in support of inequality are also discussed.

In the present paper, we prove that there does not exist any \(\mathcal {P}\mathcal {R}\)-semi-slant warped product submanifolds in paracosymplectic manifolds. In addition, by presenting a non-trivial example we find that there is no proper \(\mathcal {P}\mathcal {R}\)-semi-slant warped product submanifold other than \(\mathcal {P}\mathcal {R}\)-semi-invariant warped products.

This research presents an efficient and highly accurate cubic B-spline method (CBSM) for solving second-order linear boundary value problems (BVPs). The method achieves sixth-order convergence, supported by rigorous error analysis, ensuring rapid error reduction with mesh refinement. The effectiveness of the CBSM is validated through four numerical examples, showcasing its accuracy, reliability, and computational efficiency, making it well-suited for large-scale problems. A comparative analysis with existing methods confirms the superior performance of the CBSM, positioning it as a practical and powerful tool for solving second-order BVPs.