Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach. Solving PDEs in C + + can be used as a textbook in courses on C + + with the application, C + + in the field of engineering, numerical analysis, and numerical PDEs at the advanced undergraduate and postgraduate level. Chapter 1: Introduction to C, Chapter 2: Introduction to C + +; Chapter 3: Data Structures: Part II: Object-Oriented Approach. Chapter 4: Object-Oriented Programming: Chapter 5: Algorithm and Implementation of Object-Oriented them; Chapter 6: Object-Oriented Analysis, Part III: Partial Differential Equations and Discretization of them. Chapter 7: Convection-diffusion equation; Chapter 8: Stability Analysis 209; Chapter 9: Nonlinear Equations, Chapter 10: Applications in Image Processing: Part IV: Finite Element Discretization Method. Chapter 11: Formulation weak; Chapter 12: Finite Element Linear; Chapter 13: Finite Element Unstructured-meshes; Chapter 14: Improvement of Adaptive Mesh; Chapter 15: High-Order Finite Element; V Parts: Numerical Solution of Sparse Linear System of Equations. Chapter 16: Matrix Rare and their implementation; Chapter 17: Design Method for Large Sparse Linear Systems, Chapter 18: Parallelism, Part VI: Applications. Chapter 19: Diffusion Equation, Chapter 20: Elasticity Linear Equations; Chapter 21: Equation Stokes; Chapter 22: Electromagnetic Waves, Appendix, Bibliography, Index.